GCSE · Chapter 6
Resistance and I-V characteristics
By the end of this chapter you will be able to
- Calculate resistance, current and pd using R = V / I
- Read an I-V graph and find the resistance at a point
- Explain the shape of the I-V graph for a filament lamp and for a diode
- Describe how resistance changes for a wire, a thermistor and an LDR
You should already know
- Current, charge and potential difference (Chapter 5)
- Gradients of straight-line graphs (KS3 Maths)
Where this leads
- Series and parallel circuits and energy in circuits (Chapter 7)
- Mains supply and fuses (Chapter 8)
GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Use R = V / I to calculate resistance, current and potential difference, Explain what affects the resistance of a wire: length, cross-sectional area and temperature, Interpret I-V graphs for a fixed resistor, a filament lamp and a diode, Explain how a thermistor and an LDR change resistance with temperature and light, Plan and carry out an investigation of I-V characteristics and of the resistance of a length of wire.
Exercise P Do you remember?
1
FA pd of 6 V moves 2 C of charge. How much energy is transferred? Write the number of joules.
12
Method. Use E = Q x V.
- Multiply. E = 2 x 6 = 12 J.2 x 6 = 12
- Write the answer. 12
Check. 12 / 6 = 2 C. ✓
2
FA current of 0.5 A flows for 10 s. How much charge passes? Write the number of coulombs.
5
Method. Use Q = I x t.
- Multiply. Q = 0.5 x 10 = 5 C.0.5 x 10 = 5
- Write the answer. 5
Check. 5 / 10 = 0.5 A. ✓
3
FWhat is the unit of potential difference? Write the unit.
volt
Method. Recall the unit.
- Recall. Potential difference is measured in volts, V.volt (V)
- Write the answer. volt
Check. ✓
4
FWhich meter is connected in parallel with a component to measure its pd? Write ammeter or voltmeter.
voltmeter
Method. Recall how each meter is connected.
- Recall. A voltmeter is connected in parallel across the component.voltmeter
- Write the answer. voltmeter
Check. ✓
5
FWhat is 4 divided by 0.8? Write the number.
5
Method. Divide the two numbers.
- Divide. 4 / 0.8 = 40 / 8 = 5.4 / 0.8 = 5
- Write the answer. 5
Check. 5 x 0.8 = 4. ✓
6.1
Resistance and R = V / I
Video lesson: Resistance and R = V / IComing soon
Context. Ruby tests a small resistor. She connects a cell and an ammeter, then reads the voltmeter across the resistor. “How hard is it for the current to get through?” she asks. The answer is the resistance. It tells us how much pd is needed to push a given current through a component.
Resistance is the opposition to the flow of current. It is measured in ohms (Ω). For many components, the resistance is found from the pd and the current:
R = V / I, so V = I x R and I = V / R
A component with a high resistance needs a large pd to drive a given current through it. At a fixed temperature, a fixed resistor keeps the same resistance whatever the pd.
| Quantity | Symbol | Unit |
|---|---|---|
| resistance | R | ohm (Ω) |
| potential difference | V | volt (V) |
| current | I | ampere (A) |
The three quantities in R = V / I, with units
Key ideas
- R = V / I. Resistance in ohms (Ω), pd in volts, current in amperes.
- V = I x R and I = V / R are rearrangements of the same equation.
- A larger resistance gives a smaller current for the same pd.
- Convert milliamperes to amperes before you calculate (1 mA = 0.001 A).
Worked example 6.1.1
A resistor has a pd of 6 V across it and a current of 0.5 A flows. Calculate its resistance. Write the number of ohms.
Method. Use R = V / I.
- Take the numbers. V = 6 V and I = 0.5 A.V = 6, I = 0.5
- Divide. R = 6 / 0.5 = 12 Ω.6 / 0.5 = 12
- Write the answer. 12 Ω
Check. 0.5 x 12 = 6 V. ✓
Worked example 6.1.2
A 15 Ω resistor has a pd of 3 V across it. Calculate the current. Write the number of amperes.
Method. Use I = V / R.
- Take the numbers. V = 3 V and R = 15 Ω.V = 3, R = 15
- Divide. I = 3 / 15 = 0.2 A.3 / 15 = 0.2
- Write the answer. 0.2 A
Check. 0.2 x 15 = 3 V. ✓
Worked example 6.1.3
A 3 Ω resistor carries a current of 3 A. Calculate the pd across it. Write the number of volts.
Method. Use V = I x R.
- Take the numbers. I = 3 A and R = 3 Ω.I = 3, R = 3
- Multiply. V = 3 x 3 = 9 V.3 x 3 = 9
- Write the answer. 9 V
Check. 9 / 3 = 3 A. ✓
Watch out
Watch out: resistance is V divided by I, not I divided by V. Put the pd on top.
Exam tip
Exam tip. Write the equation and the rearrangement you need before you substitute the numbers. Give the unit, Ω.
Exercise 6A Calculating R, V and I
1
FA resistor has a pd of 10 V and a current of 2 A. Calculate its resistance. Write the number of ohms.
5
Method. Use R = V / I.
- Divide. R = 10 / 2 = 5 Ω.10 / 2 = 5
- Write the answer. 5 Ω
Check. 2 x 5 = 10 V. ✓
2
FA resistor of 8 Ω has a pd of 4 V across it. Calculate the current. Write the number of amperes.
0.5
Method. Use I = V / R.
- Divide. I = 4 / 8 = 0.5 A.4 / 8 = 0.5
- Write the answer. 0.5 A
Check. 0.5 x 8 = 4 V. ✓
3
FA resistor of 4 Ω carries 2 A. Calculate the pd across it. Write the number of volts.
8
Method. Use V = I x R.
- Multiply. V = 2 x 4 = 8 V.2 x 4 = 8
- Write the answer. 8 V
Check. 8 / 4 = 2 A. ✓
4
FA resistor of 20 Ω has a current of 0.3 A. Calculate the pd. Write the number of volts.
6
Method. Use V = I x R.
- Multiply. V = 0.3 x 20 = 6 V.0.3 x 20 = 6
- Write the answer. 6 V
Check. 6 / 20 = 0.3 A. ✓
5
FA component has a pd of 12 V and a current of 0.04 A. Calculate its resistance. Write the number of ohms.
300
Method. Use R = V / I.
- Divide. R = 12 / 0.04 = 300 Ω.12 / 0.04 = 300
- Write the answer. 300 Ω
Check. 0.04 x 300 = 12 V. ✓
6
PSA 100 mA current flows through a 50 Ω resistor. Calculate the pd. Write the number of volts.
5
Method. Convert 100 mA to amperes, then use V = I x R.
- Convert. 100 mA = 0.1 A.0.1 A
- Multiply. V = 0.1 x 50 = 5 V.0.1 x 50 = 5
- Write the answer. 5 V
Check. 5 / 50 = 0.1 A. ✓
7
PSA resistor has a pd of 9 V and draws a current of 300 mA. Calculate its resistance. Write the number of ohms.
30
Method. Convert the current, then use R = V / I.
- Convert. 300 mA = 0.3 A.0.3 A
- Divide. R = 9 / 0.3 = 30 Ω.9 / 0.3 = 30
- Write the answer. 30 Ω
Check. 0.3 x 30 = 9 V. ✓
8
PSA resistor of 2.5 kΩ (2500 Ω) has a pd of 5 V. Calculate the current in milliamperes. Write the number of milliamperes.
2
Method. Find the current in amperes first, then convert.
- Divide. I = 5 / 2500 = 0.002 A.5 / 2500 = 0.002
- Convert. 0.002 A = 2 mA.2 mA
- Write the answer. 2 mA
Check. 2 mA x 2500 = 5 V. ✓
9
FTwo resistors are each 6 Ω. Each has 3 V across it. What is the current through each? Write the number of amperes.
0.5
Method. Use I = V / R for one resistor.
- Divide. I = 3 / 6 = 0.5 A.3 / 6 = 0.5
- Write the answer. 0.5 A
Check. ✓
10
FA resistor has a resistance of 40 Ω. How much pd is needed to make a current of 0.25 A flow? Write the number of volts.
10
Method. Use V = I x R.
- Multiply. V = 0.25 x 40 = 10 V.0.25 x 40 = 10
- Write the answer. 10 V
Check. 10 / 40 = 0.25 A. ✓
11
FA lamp has a resistance of 12 Ω and is connected to 6 V. Calculate the current. Write the number of amperes.
0.5
Method. Use I = V / R.
- Divide. I = 6 / 12 = 0.5 A.6 / 12 = 0.5
- Write the answer. 0.5 A
Check. 0.5 x 12 = 6 V. ✓
12
RA pupil says that a resistor with a large resistance lets a larger current flow. Explain why this is wrong, in one sentence. Accept any sentence that says a larger resistance gives a smaller current for the same pd.
Accept any sentence that says a larger resistance gives a smaller current for the same pd.
Method. Use I = V / R.
- Look. If R is bigger, V / R is smaller for the same V.I = V / R
- Link. So a larger resistance gives a smaller current.smaller
- Write the answer. Accept any sentence that says a larger resistance gives a smaller current for the same pd.
Check. ✓
13
PSA resistor of 5 Ω is connected to a 10 V supply. A second resistor of 10 Ω replaces it. Which resistor gives the larger current? Write 5 or 10.
5
Method. Calculate both currents.
- First. I = 10 / 5 = 2 A.2 A
- Second. I = 10 / 10 = 1 A.1 A
- Compare. 2 A is larger than 1 A.5 ohm gives 2 A
- Write the answer. 5
Check. ✓
14
PSA resistor carries a current of 0.75 A when the pd is 3 V. Calculate its resistance. Write the number of ohms.
4
Method. Use R = V / I.
- Divide. R = 3 / 0.75 = 4 Ω.3 / 0.75 = 4
- Write the answer. 4 Ω
Check. 0.75 x 4 = 3 V. ✓
15
PSExplain why a 2 A current through a 100 Ω resistor needs a 200 V supply. Write the number of volts needed.
200
Method. Use V = I x R.
- Multiply. V = 2 x 100 = 200 V.2 x 100 = 200
- Write the answer. 200 V
Check. 200 / 100 = 2 A. ✓
6.2
What affects the resistance of a wire
Video lesson: What affects the resistance of a wireComing soon
Context. An electrician needs a long cable to run a lamp in a garden shed. He asks: “If I double the length, does the resistance double?” To answer, we look at what changes the resistance of a wire.
The resistance of a metal wire depends on three things:
- Length. The longer the wire, the greater the resistance. For a wire at constant temperature, the resistance is proportional to the length.
- Cross-sectional area. A thicker wire has a larger area, so there is more room for the charge to flow, and the resistance is lower.
- Temperature. In a metal, the resistance increases as the temperature increases, because the particles vibrate more and get in the way of the electrons.
Resistance against length for a wire of fixed diameter and temperature: a straight line through the origin
Key ideas
- Resistance is proportional to length (at fixed area and temperature).
- Resistance is inversely proportional to the cross-sectional area (a thicker wire has lower resistance).
- Resistance of a metal wire increases with temperature.
- Only a fixed temperature is assumed when comparing wires.
Worked example 6.2.1
A wire 20 cm long has a resistance of 2 Ω. What is the resistance of a 60 cm wire of the same material and thickness? Write the number of ohms.
Method. Resistance is proportional to length.
- Scale. 60 cm is 3 times 20 cm, so the resistance is 3 times bigger.60 / 20 = 3
- Multiply. R = 3 x 2 = 6 Ω.3 x 2 = 6
- Write the answer. 6 Ω
Check. 6 / 60 = 0.1 per cm, and 2 / 20 = 0.1 per cm. ✓
Worked example 6.2.2
A 50 cm length of wire has a resistance of 5 Ω. A 100 cm length of the same wire is used. Calculate its resistance. Write the number of ohms.
Method. Double the length to double the resistance.
- Ratio. 100 cm is 2 times 50 cm.100 / 50 = 2
- Multiply. R = 2 x 5 = 10 Ω.2 x 5 = 10
- Write the answer. 10 Ω
Check. 10 / 100 = 0.1 Ω per cm. ✓
Worked example 6.2.3
A wire has a resistance of 4 Ω at 20 cm long and is replaced with one of double the cross-sectional area and the same length. Explain the change in resistance. Write the new resistance in ohms.
Method. Use the rule: resistance is inversely proportional to area.
- Area. Doubling the area halves the resistance.area x 2
- Result. R = 4 / 2 = 2 Ω.4 / 2 = 2
- Write the answer. 2 Ω
Check. A thicker wire has more room for the charge. ✓
Watch out
Watch out: a longer wire has a bigger resistance, but a thicker wire has a smaller one. Length and thickness have opposite effects.
Exam tip
Practical safety. Use a low-voltage supply, keep the wire on a safe surface and let it cool between readings. Never use mains voltage.
Exercise 6B Length, area and temperature
1
FA wire of 30 cm has a resistance of 3 Ω. What is the resistance of 60 cm of the same wire? Write the number of ohms.
6
Method. Resistance is proportional to length.
- Double. 60 cm is twice 30 cm, so R doubles.2 x 3 = 6
- Write the answer. 6 Ω
Check. ✓
2
FA 100 cm length of wire has a resistance of 10 Ω. What is the resistance of 40 cm? Write the number of ohms.
4
Method. Find the resistance per cm.
- Per cm. Resistance per cm = 10 / 100 = 0.1 Ω.0.1
- Multiply. 40 x 0.1 = 4 Ω.40 x 0.1 = 4
- Write the answer. 4 Ω
Check. ✓
3
FA wire is replaced by one with twice the cross-sectional area. What happens to the resistance: double, halve or stay the same? Write the word.
halve
Method. Resistance is inversely proportional to area.
- Recall. A thicker wire has more room for the charge, so its resistance halves.halve
- Write the answer. halve
Check. ✓
4
FWhich change makes a wire have a larger resistance: a longer wire or a thicker wire? Write longer or thicker.
longer
Method. Think about each quantity.
- Compare. A longer wire has more resistance; a thicker wire has less.longer
- Write the answer. longer
Check. ✓
5
FThe temperature of a metal wire increases. What happens to its resistance: increase, decrease or stay the same? Write the word.
increase
Method. Think about the particles in the metal.
- Recall. The particles vibrate more, so they get in the way of the electrons, and the resistance increases.increase
- Write the answer. increase
Check. ✓
6
PSA wire of length 80 cm has resistance 8 Ω. Calculate the resistance of a 25 cm length of the same wire. Write the number of ohms.
2.5
Method. Find the resistance per cm, then multiply by 25.
- Per cm. 8 / 80 = 0.1 Ω per cm.0.1
- Multiply. 25 x 0.1 = 2.5 Ω.25 x 0.1 = 2.5
- Write the answer. 2.5 Ω
Check. 2.5 / 25 = 0.1. ✓
7
RIn an investigation, a student measures the resistance of 10 cm, 20 cm, 30 cm and 40 cm of the same wire. The readings are 1, 2, 3 and 4 Ω. Describe the relationship. Write one sentence: the relationship is ... Accept any sentence that says resistance is proportional to length.
Accept any sentence that says resistance is proportional to length.
Method. Look at how the values change.
- Look. Each 10 cm adds 1 Ω, so R is directly proportional to length.proportional
- Write the answer. Accept any sentence that says resistance is proportional to length.
Check. ✓
8
RA pupil says “doubling the length doubles the resistance, so halving the diameter halves it.” Explain why the second half is wrong. Accept any answer that says halving the diameter reduces the area to a quarter, so the resistance quadruples.
Accept any answer that says halving the diameter reduces the area to a quarter, so the resistance quadruples.
Method. Think about the area of the wire.
- Area. Halving the diameter gives a quarter of the area, since area depends on diameter squared.quarter area
- Resistance. So the resistance is four times bigger, not half.four times
- Write the answer. Accept any answer that says halving the diameter reduces the area to a quarter, so the resistance quadruples.
Check. ✓
9
RPlan a fair test to find the resistance of a length of wire. Name two things you would keep the same, and one thing you would change. Accept any answer with: keep the wire type and temperature the same; change the length.
Accept any answer with: keep the wire type and temperature the same; change the length.
Method. Think about which variable you change.
- Change. Change the length of the wire, the independent variable.length
- Keep. Keep the wire type, diameter and temperature the same.same wire
- Write the answer. Accept any answer with: keep the wire type and temperature the same; change the length.
Check. ✓
10
PSA 60 cm wire has resistance 6 Ω. A 90 cm length of the same wire is used. Calculate its resistance. Write the number of ohms.
9
Method. Scale by the ratio of lengths.
- Ratio. 90 / 60 = 1.5.1.5
- Multiply. R = 1.5 x 6 = 9 Ω.1.5 x 6 = 9
- Write the answer. 9 Ω
Check. ✓
11
FA thin wire and a thick wire of the same length and material are compared. Which has the lower resistance? Write thin or thick.
thick
Method. Think about how area affects the flow of charge.
- Recall. The thick wire has the larger area, so it has the lower resistance.thick
- Write the answer. thick
Check. ✓
6.3
I-V characteristics
Video lesson: I-V characteristicsComing soon
Context. Tom wants to know how a lamp behaves when the pd is increased. He plots the current against pd for three components: a fixed resistor, a filament lamp and a diode. Each graph has a different shape, and the shape tells us how the resistance changes.
An I-V graph plots current (on the y-axis) against pd (on the x-axis). The resistance at any point is R = V / I, which is the reciprocal of the gradient for a straight line through the origin:
- Fixed resistor (at constant temperature): a straight line through the origin. Its resistance is constant.
- Filament lamp: a curve. As the current rises, the filament gets hotter and its resistance increases, so the curve flattens.
- Diode: current flows only in the forward direction, and only above about 0.6 V. In the reverse direction the current is zero.
I-V graphs for a fixed resistor (blue), a filament lamp (orange) and a diode (green)
The circuit for an I-V investigation: vary the pd and record the current and voltage
Key ideas
- Straight line through the origin: constant resistance.
- Filament lamp: resistance increases as the temperature rises.
- Diode: current flows only in the forward direction, above about 0.6 V.
- Resistance at a point = V / I at that point.
Worked example 6.3.1
On the I-V graph, a resistor gives a current of 0.8 A at a pd of 4 V. Calculate its resistance. Write the number of ohms.
Method. Use R = V / I at the point.
- Take the numbers. V = 4 V and I = 0.8 A.V = 4, I = 0.8
- Divide. R = 4 / 0.8 = 5 Ω.4 / 0.8 = 5
- Write the answer. 5 Ω
Check. 0.8 x 5 = 4 V. ✓
Worked example 6.3.2
Explain why the filament lamp graph curves. Write one reason in one sentence. Accept any sentence that says the resistance increases as the filament gets hotter.
Method. Think about the filament.
- Look. As the current increases, the filament gets hotter.hotter
- Link. Hotter metal has more resistance, so the current rises more slowly than the pd.slower rise
- Write the answer. Accept any sentence that says the resistance increases as the filament gets hotter.
Check. ✓
Worked example 6.3.3
A diode is connected the wrong way round in a circuit. What is the current? Write the number of amperes.
Method. A diode allows current only in one direction.
- Look. In the reverse direction the diode has a very high resistance.reverse
- Decide. So almost no current flows.zero
- Write the answer. 0
Check. The diode graph is flat at zero in the reverse direction. ✓
Watch out
Watch out: a filament lamp curve is not a straight line, so its resistance is not constant. Use the value of V / I at the point you are asked about.
Exam tip
Exam tip. For an I-V graph, say which of the three shapes you can see, then say whether the resistance is constant, increasing or infinite.
Exercise 6C Reading I-V graphs
1
FWhich component has an I-V graph that is a straight line through the origin? Write the component.
fixed resistor
Method. Recall the shape for a resistor at constant temperature.
- Recall. A fixed resistor gives a straight line through the origin.straight line
- Write the answer. fixed resistor
Check. ✓
2
FWhich component has resistance that increases as the current increases? Write the component.
filament lamp
Method. Think about what happens to a filament as it heats.
- Recall. The filament gets hotter, so its resistance rises.filament lamp
- Write the answer. filament lamp
Check. ✓
3
FWhich component allows current to flow in one direction only? Write the component.
diode
Method. Recall the component.
- Recall. A diode allows current to flow one way only.diode
- Write the answer. diode
Check. ✓
4
PSOn a graph, a straight line through the origin has a constant gradient. For a resistor, what does the gradient represent? Write the word: current or resistance.
resistance
Method. For I-V, the gradient is I divided by V, which is the reciprocal of R.
- Look. The gradient of the I-V line is 1/R, so the gradient is the reciprocal of the resistance.1/R
- Write the answer. resistance
Check. The gradient of I against V is 1 / R. ✓
5
FIn the I-V graph, a resistor carries 0.6 A at 3 V. Calculate its resistance. Write the number of ohms.
5
Method. Use R = V / I.
- Divide. R = 3 / 0.6 = 5 Ω.3 / 0.6 = 5
- Write the answer. 5 Ω
Check. 0.6 x 5 = 3 V. ✓
6
PSA filament lamp carries 1 A at 2 V, and 2 A at 6 V. Calculate the resistance at each point, and say whether it increases or decreases. Write the two resistances, separated by a comma.
2, 3
Method. Use R = V / I at each point.
- First point. R = 2 / 1 = 2 Ω.2 / 1 = 2
- Second point. R = 6 / 2 = 3 Ω, so the resistance has increased.6 / 2 = 3
- Write the answer. 2, 3
Check. The resistance increases as the lamp heats. ✓
7
FA diode is forward biased. Above about 0.6 V, does the current increase steeply or stay at zero? Write steeply or zero.
steeply
Method. Look at the diode curve.
- Recall. Above about 0.6 V the diode conducts and the current rises steeply.steeply
- Write the answer. steeply
Check. ✓
8
FA diode is reverse biased. What is the current? Write the number of amperes.
0
Method. A diode blocks current in the reverse direction.
- Recall. In reverse bias the current is zero.0 A
- Write the answer. 0
Check. ✓
9
RExplain why the resistance of a diode is not constant, in one sentence. Accept any sentence that says the resistance falls sharply once the forward pd passes about 0.6 V.
Accept any sentence that says the resistance falls sharply once the forward pd passes about 0.6 V.
Method. Think about the shape of the curve.
- Shape. The curve is flat then steep.flat then steep
- Link. So the resistance changes with the pd.changes
- Write the answer. Accept any sentence that says the resistance falls sharply once the forward pd passes about 0.6 V.
Check. ✓
10
RA student uses a fixed resistor and draws its I-V graph. The graph is a straight line through the origin. What does this tell us? Accept any sentence that says the resistance is constant, so the current is proportional to the pd.
Accept any sentence that says the resistance is constant, so the current is proportional to the pd.
Method. Think about the shape of the line.
- Shape. A straight line through the origin means I is proportional to V.proportional
- Meaning. So the resistance is constant.constant R
- Write the answer. Accept any sentence that says the resistance is constant, so the current is proportional to the pd.
Check. ✓
11
RIn the investigation, the pd is increased from 0 V to 6 V. Describe the shape of the I-V graph for a filament lamp and say why, in two sentences. Accept any answer that says it is a curve, and the resistance increases because the filament gets hotter.
Accept any answer that says it is a curve, and the resistance increases because the filament gets hotter.
Method. Describe the shape and the reason.
- Shape. The graph is a curve that becomes less steep as the pd rises.curve
- Reason. The filament heats up, so its resistance increases.resistance increases
- Write the answer. Accept any answer that says it is a curve, and the resistance increases because the filament gets hotter.
Check. ✓
12
PSA resistor and a filament lamp are on the same I-V graph. Both pass through (2 V, 0.4 A). Find the resistance at this point. Write the number of ohms.
5
Method. Use R = V / I at the common point.
- Divide. R = 2 / 0.4 = 5 Ω.2 / 0.4 = 5
- Write the answer. 5 Ω
Check. 0.4 x 5 = 2 V. ✓
13
RPlan an investigation of the I-V graph for a filament lamp. Name the two meters you need, and say how each is connected. Write the answer: ammeter in series, voltmeter in parallel.
ammeter in series, voltmeter in parallel
Method. Recall how each meter is connected.
- Ammeter. The ammeter is connected in series with the lamp.series
- Voltmeter. The voltmeter is connected in parallel across the lamp.parallel
- Write the answer. ammeter in series, voltmeter in parallel
Check. ✓
6.4
Thermistors and light-dependent resistors
Video lesson: Thermistors and light-dependent resistorsComing soon
Context. A fire alarm needs to respond to heat. A light sensor on a street lamp must switch on when it gets dark. Both use a component whose resistance changes with a physical quantity. These are called sensors.
A thermistor is a resistor whose resistance falls as its temperature rises. An LDR (light-dependent resistor) has a resistance that falls when the light falling on it gets brighter. We use these in circuits to switch things on and off, or to measure temperature or light. A potential divider circuit of two resistors can turn the change in resistance into a change in pd.
| Component | What changes | Effect on resistance | Use |
|---|---|---|---|
| thermistor | temperature rises | resistance falls | temperature sensor, fire alarm, thermostat |
| LDR | light gets brighter | resistance falls | light sensor, street lamp switching |
| filament lamp | current rises (so the filament gets hotter) | resistance rises | lamps, shown by a curved I-V graph |
| fixed resistor | temperature stays constant | resistance does not change | standard component, straight I-V line |
| diode | pd in the forward direction | resistance falls sharply above about 0.6 V | lets current flow one way only |
How thermistors, LDRs and other components behave
Key ideas
- Thermistor: resistance falls as the temperature rises.
- LDR: resistance falls as the light gets brighter.
- Sensors use the change in resistance to switch circuits or to measure.
- A fixed resistor does not change with temperature or light.
Worked example 6.4.1
In the dark, an LDR has a resistance of 10 kΩ. In bright light it has 1 kΩ. In which condition is the current larger for the same pd? Write dark or bright.
Method. Use I = V / R: a smaller resistance gives a larger current.
- Compare. The LDR has 1 kΩ in bright light, which is less than 10 kΩ in the dark.1 < 10
- Decide. So the current is larger in bright light.bright
- Write the answer. bright
Check. For the same pd, a smaller R gives a bigger I. ✓
Worked example 6.4.2
A thermistor resistance falls from 400 Ω to 100 Ω when it gets hotter. How many times smaller is the new resistance? Write the number.
Method. Divide the old resistance by the new one.
- Read. Old resistance = 400 Ω, new resistance = 100 Ω.400, 100
- Divide. 400 / 100 = 4.400 / 100 = 4
- Write the answer. 4
Check. 100 x 4 = 400. ✓
Worked example 6.4.3
Which component has a resistance that falls as its temperature rises: a thermistor or a fixed resistor? Write the name.
Method. Recall how a thermistor behaves.
- Look. A fixed resistor keeps the same resistance at constant temperature.constant
- Decide. The thermistor is the component whose resistance falls as it heats up.thermistor
- Write the answer. thermistor
Check. ✓
Watch out
Watch out: a thermistor and an LDR both have falling resistance as the quantity increases. Do not say the thermistor resistance increases with temperature.
Exam tip
Exam tip. When explaining a sensor, say which way the resistance changes, then say what that does to the current or the pd.
Exercise 6D Sensors and resistance
1
FWhat happens to the resistance of a thermistor when its temperature rises: rises or falls? Write the word.
falls
Method. Recall how a thermistor behaves.
- Recall. A thermistor has a lower resistance when it is hot.falls
- Write the answer. falls
Check. ✓
2
FWhat happens to the resistance of an LDR when the light gets brighter: rises or falls? Write the word.
falls
Method. Recall how an LDR behaves.
- Recall. An LDR has a lower resistance in brighter light.falls
- Write the answer. falls
Check. ✓
3
FName a use of a thermistor. Write the use in a few words.
fire alarm
Method. Think about where a temperature sensor is needed.
- Recall. A thermistor is used in a fire alarm or a thermostat.fire alarm
- Write the answer. fire alarm
Check. Accept thermostat, or a temperature sensor, too. ✓
4
FName a use of an LDR. Write the use in a few words.
street light
Method. Think about where light is sensed.
- Recall. An LDR can switch a street lamp on when it gets dark.street lamp
- Write the answer. street light
Check. Accept a light sensor or a night light. ✓
5
FAn LDR is in a circuit. The room is dark. Is the LDR resistance high or low? Write high or low.
high
Method. Think about light and resistance.
- Recall. In the dark the LDR has a high resistance.high
- Write the answer. high
Check. ✓
6
PSA thermistor has a resistance of 200 Ω when cold and 50 Ω when hot. How many times bigger is the cold resistance? Write the number.
4
Method. Divide the cold resistance by the hot resistance.
- Divide. 200 / 50 = 4.200 / 50 = 4
- Write the answer. 4
Check. 50 x 4 = 200. ✓
7
PSIn a circuit with a fixed pd, an LDR goes from 500 Ω in the dark to 100 Ω in bright light. Which gives the larger current? Write dark or bright.
bright
Method. Smaller resistance gives larger current for the same pd.
- Compare. 100 Ω is less than 500 Ω, so the current is larger in bright light.bright
- Write the answer. bright
Check. ✓
8
RExplain how a thermistor could be used in a circuit to switch on a fan when the room gets hot, in one sentence. Accept any sentence that says the thermistor resistance falls, so the current or pd changes enough to switch the fan on.
Accept any sentence that says the thermistor resistance falls, so the current or pd changes enough to switch the fan on.
Method. Think about the chain of effects.
- Resistance. As the room gets hot, the thermistor resistance falls.resistance falls
- Switch. This changes the current or pd, which switches on the fan.switches on
- Write the answer. Accept any sentence that says the thermistor resistance falls, so the current or pd changes enough to switch the fan on.
Check. ✓
9
RExplain why a filament lamp is not a good thermistor. Accept any answer that says the filament resistance increases with temperature, the opposite of a thermistor.
Accept any answer that says the filament resistance increases with temperature, the opposite of a thermistor.
Method. Compare the two behaviours.
- Lamp. A filament lamp has a resistance that increases as it gets hotter.increases
- Thermistor. A thermistor has a resistance that falls as it gets hotter.falls
- Write the answer. Accept any answer that says the filament resistance increases with temperature, the opposite of a thermistor.
Check. ✓
10
RAn LDR and a fixed resistor are in series with a cell. The room gets brighter. Explain what happens to the current, in one sentence. Accept any sentence that says the LDR resistance falls, so the current increases.
Accept any sentence that says the LDR resistance falls, so the current increases.
Method. Think about the total resistance.
- Total. The LDR resistance falls, so the total resistance falls.total falls
- Current. For the same pd, the current increases.current increases
- Write the answer. Accept any sentence that says the LDR resistance falls, so the current increases.
Check. ✓
Chapter summary
| Skill | Method |
|---|---|
| Calculate R, V or I | R = V / I; V = I x R; I = V / R |
| Wire resistance | Proportional to length; inversely proportional to area; increases with temperature |
| Read an I-V graph | Resistor: straight line; lamp: curve; diode: one-way, above 0.6 V |
| Sensors | Thermistor and LDR: resistance falls as temperature or light increases |
Can you…?
- I can use R = V / I to find R, V or I
- I can describe what changes the resistance of a wire
- I can recognise the three I-V graph shapes and explain them
- I can describe how a thermistor and an LDR behave
- I can plan an I-V investigation with a low-voltage supply
Key terms
- resistance
- opposition to the flow of current; R = V / I, in ohms (Ω)
- ohm (Ω)
- the unit of resistance: 1 volt per ampere
- I-V characteristic
- a graph of current against potential difference for a component
- filament lamp
- a lamp whose resistance rises as its filament gets hotter
- diode
- a component that allows current to flow in one direction only
- thermistor
- a resistor whose resistance falls as its temperature rises
- LDR
- a light-dependent resistor whose resistance falls in brighter light
Exercise 6Z Check-up
1
Calculate the resistance of a component with a pd of 8 V and a current of 2 A. Write the number of ohms.
4
Method. Use R = V / I.
- Divide. R = 8 / 2 = 4 Ω.8 / 2 = 4
- Write the answer. 4 Ω
Check. ✓
2
A resistor of 10 Ω has a current of 0.6 A. Calculate the pd. Write the number of volts.
6
Method. Use V = I x R.
- Multiply. V = 0.6 x 10 = 6 V.0.6 x 10 = 6
- Write the answer. 6 V
Check. ✓
3
A wire of 10 cm has a resistance of 1 Ω. What is the resistance of 50 cm of the same wire? Write the number of ohms.
5
Method. Resistance is proportional to length.
- Scale. 50 / 10 = 5, so R = 5 Ω.50 / 10 = 5
- Write the answer. 5 Ω
Check. ✓
4
Which component has a straight-line I-V graph through the origin: fixed resistor or filament lamp? Write the name.
fixed resistor
Method. Recall the shapes.
- Recall. The fixed resistor graph is a straight line through the origin.fixed resistor
- Write the answer. fixed resistor
Check. ✓
5
What happens to the resistance of a metal wire as its temperature rises: increases or decreases? Write the word.
increases
Method. Think about the particles.
- Recall. The metal particles vibrate more, so resistance increases.increases
- Write the answer. increases
Check. ✓
6
A 2 A current flows through a 15 Ω resistor. Calculate the pd. Write the number of volts.
30
Method. Use V = I x R.
- Multiply. V = 2 x 15 = 30 V.2 x 15 = 30
- Write the answer. 30 V
Check. ✓
7
Name the component that has a resistance that falls when light falls on it. Write the name.
LDR
Method. Recall the light sensor.
- Recall. An LDR has a resistance that falls when the light is brighter.LDR
- Write the answer. LDR
Check. ✓
8
A diode is forward biased and the pd is 0.3 V. Is the current zero or steady at a larger value? Write zero or larger.
zero
Method. The diode does not conduct below about 0.6 V.
- Recall. Below about 0.6 V the forward current is effectively zero.zero
- Write the answer. zero
Check. ✓
9
A resistance of 4 Ω is replaced by 8 Ω with the same pd. How does the current change: doubles or halves? Write the word.
halves
Method. Use I = V / R.
- Compare. Doubling R halves the current for the same V.halves
- Write the answer. halves
Check. ✓
10
Explain why the resistance of the filament lamp increases as the current rises. Accept any answer that says the filament gets hotter, and the resistance of metal increases with temperature.
Accept any answer that says the filament gets hotter, and the resistance of metal increases with temperature.
Method. Think about the filament.
- Hot. The current heats the filament.hot
- Resistance. Metal resistance increases with temperature.increases
- Write the answer. Accept any answer that says the filament gets hotter, and the resistance of metal increases with temperature.
Check. ✓
Total 32 marks. Allow about 32 minutes.
Exercise 6X Exam-style questions
1
FCalculate the resistance of a resistor with a pd of 12 V across it and a current of 3 A. Write the number of ohms.[2 marks]
4
Method. Use R = V / I.
- Divide. R = 12 / 3 = 4 Ω.12 / 3 = 4
- Write the answer. 4 Ω
Check. ✓
2
FA resistor has a resistance of 25 Ω. Calculate the current when the pd is 5 V. Write the number of amperes.[2 marks]
0.2
Method. Use I = V / R.
- Divide. I = 5 / 25 = 0.2 A.5 / 25 = 0.2
- Write the answer. 0.2 A
Check. ✓
3
PSA wire of length 25 cm has a resistance of 2.5 Ω. Calculate the resistance of a 75 cm length of the same wire. Write the number of ohms.[2 marks]
7.5
Method. Scale by the length ratio.
- Ratio. 75 / 25 = 3.3
- Multiply. R = 3 x 2.5 = 7.5 Ω.3 x 2.5 = 7.5
- Write the answer. 7.5 Ω
Check. ✓
4
RA student measures the current through a lamp at several pds. Describe the I-V graph you would expect for a filament lamp, and explain its shape. Accept any answer that says the graph is a curve that flattens, because the filament heats up and its resistance increases.[3 marks]
Accept any answer that says the graph is a curve that flattens, because the filament heats up and its resistance increases.
Method. Describe the shape and the reason.
- Shape. The graph is a curve that becomes less steep as the pd increases.curve, flattening
- Reason. As the current rises, the filament gets hotter.hotter
- Effect. The resistance increases, so the current rises more slowly than the pd.resistance increases
- Write the answer. Accept any answer that says the graph is a curve that flattens, because the filament heats up and its resistance increases.
Check. ✓
5
RA diode is connected in a circuit with a cell and a lamp. Explain how to connect the diode so that the lamp lights, and why the lamp does not light if the diode is reversed. Accept any answer that says the diode must be forward biased (in the direction of the arrow), and reversed it blocks the current.[3 marks]
Accept any answer that says the diode must be forward biased (in the direction of the arrow), and reversed it blocks the current.
Method. Think about the direction of the current.
- Forward. The diode must be forward biased, with its arrow in the direction of the current.forward
- Reverse. If reversed, the diode has a very high resistance, so almost no current flows.blocks
- Write the answer. Accept any answer that says the diode must be forward biased (in the direction of the arrow), and reversed it blocks the current.
Check. ✓
6
RA student plans an investigation of the resistance of a length of wire. Describe the apparatus, the readings taken and how the resistance is found. Accept any answer with a low-voltage supply, an ammeter in series, a voltmeter in parallel, several lengths, and R = V / I for each.[5 marks]
Accept any answer with a low-voltage supply, an ammeter in series, a voltmeter in parallel, several lengths, and R = V / I for each.
Method. Describe the method in order.
- Apparatus. Use a low-voltage supply, an ammeter in series with the wire, and a voltmeter in parallel across the wire.series, parallel
- Lengths. Measure the wire for several different lengths, keeping the same wire type and temperature.several lengths
- Readings. Record the voltage and the current for each length.V and I
- Calculate. Find R = V / I for each length.R = V / I
- Check. Plot R against length; a straight line through the origin shows proportionality.graph
- Write the answer. Accept any answer with a low-voltage supply, an ammeter in series, a voltmeter in parallel, several lengths, and R = V / I for each.
Check. ✓
7
RA thermistor is used in a circuit to switch on a heater when the temperature falls. Explain how the circuit works as the temperature falls. Accept any answer that says the resistance of the thermistor rises as the temperature falls, which changes the pd or current enough to switch the heater on.[4 marks]
Accept any answer that says the resistance of the thermistor rises as the temperature falls, which changes the pd or current enough to switch the heater on.
Method. Think about the thermistor when it is cold.
- Resistance. When the temperature falls, the thermistor resistance rises.rises
- Pd. The thermistor takes a larger share of the pd in a potential divider.share of pd
- Switch. This pd change switches on the heater.switches on
- Write the answer. Accept any answer that says the resistance of the thermistor rises as the temperature falls, which changes the pd or current enough to switch the heater on.
Check. ✓
8
RExplain why the I-V graph for a fixed resistor is a straight line, but the graph for a diode is not. Accept any answer that says a fixed resistor has constant resistance at constant temperature, while a diode only conducts in one direction and its resistance changes with the pd.[4 marks]
Accept any answer that says a fixed resistor has constant resistance at constant temperature, while a diode only conducts in one direction and its resistance changes with the pd.
Method. Compare the two components.
- Resistor. A fixed resistor has constant resistance at constant temperature, so I is proportional to V.constant R
- Diode. A diode conducts only in the forward direction, above about 0.6 V.one direction
- Shape. So its resistance changes with the pd, and the graph is not a straight line.not straight
- Write the answer. Accept any answer that says a fixed resistor has constant resistance at constant temperature, while a diode only conducts in one direction and its resistance changes with the pd.
Check. ✓
9
PSA 9 V cell is connected to a 3 Ω and a 6 Ω resistor one after another in a series loop. Calculate the current in the loop, if the total resistance is 9 Ω. Write the number of amperes.[3 marks]
1
Method. Add the resistances, then use I = V / R.
- Total. Total R = 3 + 6 = 9 Ω.3 + 6 = 9
- Divide. I = 9 / 9 = 1 A.9 / 9 = 1
- Write the answer. 1 A
Check. ✓
10
REvaluate the claim: “a filament lamp obeys Ohm’s law because it has a resistance, so its I-V graph is a straight line.” Explain why the claim is wrong. Accept any answer that says the lamp’s resistance changes as it heats, so its graph is a curve, not a straight line.[4 marks]
Accept any answer that says the lamp’s resistance changes as it heats, so its graph is a curve, not a straight line.
Method. Check the link between resistance and the graph.
- Ohm. A straight-line graph through the origin is needed for a constant resistance.constant R
- Lamp. The filament resistance changes as it heats up.changes
- Conclusion. So its I-V graph is a curve, and the claim is wrong.curve
- Write the answer. Accept any answer that says the lamp’s resistance changes as it heats, so its graph is a curve, not a straight line.
Check. ✓