Fixed and variable resistors, thermistors, LDRs; and the factors that determine resistance: length, cross-section, material & temperature.
AQA GCSE Physics 4.2 | Year 10 | Age 14–15
⚡ Define resistance and recall the equation R = V ÷ I
🔧 Describe how length, cross-sectional area, material and temperature affect resistance
🌡️ Explain how a thermistor's resistance changes with temperature and give a real-world application
💡 Explain how an LDR's resistance changes with light intensity and give a real-world application
🎛️ Distinguish between fixed and variable resistors and describe their uses in circuits
🧮 Calculate resistance, voltage or current using R = V ÷ I in multi-step problems
⚡ What is Resistance?
Resistance is a measure of how difficult it is for electric current to flow through a component or material. The greater the resistance, the smaller the current for a given voltage.
Resistance (R) — the ratio of the potential difference across a component to the current flowing through it. Measured in ohms (Ω).
R = V ÷ I
Resistance (Ω) = Voltage (V) ÷ Current (A)
This can be rearranged to find voltage or current:
V = I × R I = V ÷ R
Symbol
Quantity
Unit
R
Resistance
Ohms (Ω)
V
Potential difference / Voltage
Volts (V)
I
Current
Amperes (A)
A resistor that obeys Ohm's Law will have a constant resistance — that is, its current–voltage graph is a straight line through the origin.
📏 Factors Affecting Resistance
The resistance of a wire or conductor depends on four key factors:
1. Length: The longer the wire, the greater its resistance. Doubling the length doubles the resistance. Electrons collide more often along a longer path.
2. Cross-sectional Area: The thicker the wire, the lower its resistance. A wider wire provides more "lanes" for electrons to travel through, reducing collisions per electron.
3. Material (Resistivity): Different materials resist the flow of current differently. Copper has very low resistivity — it is a good conductor. Nichrome wire has much higher resistivity, making it useful for heating elements.
4. Temperature: For most metals, resistance increases as temperature increases. Hotter atoms vibrate more vigorously, causing more frequent collisions with the electrons flowing through the wire.
R ∝ Length R ∝ 1 ÷ Area
These relationships are combined in the resistivity equation (Higher Tier context):
R = ρ × L ÷ A
ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²)
Remember: longer = more resistance; thicker = less resistance; hotter metal = more resistance.
🔧 Fixed and Variable Resistors
Resistors are components designed to provide a specific resistance in a circuit. They come in two main types:
Fixed Resistor: Has a constant, unchanging resistance value. Used to limit the current through other components — for example, protecting an LED from excessive current.
Variable Resistor (Rheostat / Potentiometer): Allows the resistance to be adjusted manually by changing the length of wire in the circuit (by moving a sliding contact). Used to control brightness of lights, volume of speakers, or speed of motors.
The circuit symbol for a fixed resistor is a plain rectangle. A variable resistor has an arrow through it.
A variable resistor in a potential divider circuit can be used to give a variable output voltage — very useful in sensor circuits.
Variable resistors work on the principle that moving the slider changes the effective length of the conducting wire, and since R ∝ L, this changes the resistance. Engineers use this to create adjustable circuits without needing to swap components.
🌡️ Thermistors
A thermistor is a special resistor whose resistance changes significantly with temperature. Most thermistors used in GCSE Physics are NTC (Negative Temperature Coefficient) thermistors.
NTC Thermistor: As temperature increases, resistance decreases. (They behave opposite to a normal metal wire.)
Why does this happen? In a thermistor (a semiconductor material), increasing temperature frees up more charge carriers, making it easier for current to flow — so resistance falls. This is the opposite of what happens in a metal.
Temperature ↑ → Resistance ↓ (for NTC thermistor)
Temperature ↓ → Resistance ↑ (for NTC thermistor)
Real-world applications of thermistors:
Thermostats in central heating systems
Temperature sensors in ovens and fridges
Engine temperature warning systems in cars
Baby incubators and medical temperature monitors
In a sensor circuit, a thermistor can be paired with a fixed resistor to create a potential divider — when temperature changes, the output voltage changes, triggering an alarm or a heater.
💡 Light-Dependent Resistors (LDRs)
An LDR (Light-Dependent Resistor) is a component whose resistance changes depending on how much light falls on it.
LDR: As light intensity increases, resistance decreases. In darkness, resistance is very high (can be millions of ohms). In bright light, resistance is very low (can be hundreds of ohms).
LDRs are also semiconductor devices. More light means more energy is absorbed, freeing more charge carriers and allowing current to flow more easily — hence lower resistance in bright conditions.
Real-world applications of LDRs:
Automatic street lights (turn on when it gets dark)
Burglar alarms triggered by a beam of light being broken
Camera light meters (measuring brightness to set exposure)
Automatic brightness control on phone screens
Both thermistors and LDRs are examples of non-ohmic components — their resistance is not constant, so they do not obey Ohm's Law.
Example 1: A resistor has a voltage of 12 V across it and a current of 0.5 A flowing through it. Calculate its resistance.
1 Write down the formula: R = V ÷ I
2 Identify the values: V = 12 V, I = 0.5 A
3 Substitute: R = 12 ÷ 0.5
4 Calculate: R = 24 Ω
R = 24 Ω
Example 2: A wire has a resistance of 8 Ω. A second wire is made of the same material and has the same cross-sectional area, but is three times longer. What is the resistance of the second wire?
1 Recall the relationship: R ∝ Length (for the same material and area)
2 The second wire is 3× longer, so its resistance is 3× greater
3 R₂ = 3 × R₁ = 3 × 8 Ω
4 R₂ = 24 Ω
R₂ = 24 Ω
Example 3: A thermistor is used in a temperature-sensing circuit. At 20°C its resistance is 5 000 Ω. The supply voltage is 10 V. Calculate the current through the thermistor at 20°C. When the temperature rises to 80°C, the resistance falls to 500 Ω. Calculate the new current.
1 Use I = V ÷ R for the first temperature
2 At 20°C: I = 10 ÷ 5000 = 0.002 A = 2 mA
3 At 80°C: I = 10 ÷ 500 = 0.02 A = 20 mA
4 The current increased 10× because resistance fell 10× when temperature rose
At 20°C: I = 0.002 A (2 mA) | At 80°C: I = 0.02 A (20 mA)
Example 4: An LDR has a resistance of 1 200 Ω in dim light. A 6 V battery is connected to it in series with a fixed 300 Ω resistor. Calculate: (a) the total resistance, (b) the total current in the circuit, and (c) the voltage across the LDR.
1 (a) Total resistance in series: R_total = R_LDR + R_fixed = 1200 + 300 = 1500 Ω
2 (b) Total current: I = V ÷ R_total = 6 ÷ 1500 = 0.004 A = 4 mA
3 (c) Voltage across LDR: V_LDR = I × R_LDR = 0.004 × 1200 = 4.8 V
Question 1: Which of the following correctly states the unit of resistance?
Question 2: A thermistor is placed in a cold environment. What happens to its resistance?
Question 3: Wire X and Wire Y are made of the same material at the same temperature. Wire Y has twice the cross-sectional area of Wire X but the same length. How does the resistance of Wire Y compare to Wire X?
Question 4: A lamp has a resistance of 20 Ω and a current of 0.3 A flows through it. Calculate the voltage across the lamp. Give your answer in volts (V).
Question 5: An LDR in bright sunlight has a resistance of 200 Ω. A 5 V supply is connected directly across it. Calculate the current through the LDR. Give your answer in amperes (A).
Challenge 1: A student investigates how the resistance of a wire depends on its length. She uses a nichrome wire and measures the following data:
Length (cm)
Resistance (Ω)
10
2.4
20
4.8
30
7.2
40
9.6
(a) State the relationship between length and resistance shown by this data.
(b) Predict the resistance of a 55 cm piece of the same wire.
(c) Explain in terms of electron collisions why resistance increases with length.
(a) Resistance is directly proportional to length — when length doubles, resistance doubles (R ∝ L).
(b) Resistance per cm = 2.4 ÷ 10 = 0.24 Ω/cm. For 55 cm: R = 0.24 × 55 = 13.2 Ω.
(c) In a longer wire, electrons must travel a greater distance. As they move through the wire they collide with vibrating metal ions. A longer wire means more collisions occur, so the flow of electrons (current) is impeded more — giving greater resistance.
Challenge 2: A thermistor and a 1 000 Ω fixed resistor are connected in series with a 9 V battery. At room temperature (20°C) the thermistor has a resistance of 2 000 Ω.
(a) Calculate the total resistance of the circuit at 20°C.
(b) Calculate the current flowing through the circuit at 20°C.
(c) Calculate the voltage across the fixed resistor at 20°C.
(d) The temperature rises and the thermistor's resistance falls to 500 Ω. State and explain what happens to the voltage across the fixed resistor.
(a) R_total = 2000 + 1000 = 3000 Ω
(b) I = V ÷ R = 9 ÷ 3000 = 0.003 A (3 mA)
(c) V_fixed = I × R = 0.003 × 1000 = 3 V
(d) New R_total = 500 + 1000 = 1500 Ω. New I = 9 ÷ 1500 = 0.006 A. New V_fixed = 0.006 × 1000 = 6 V. The voltage across the fixed resistor increases. As temperature rises, the thermistor's resistance falls, so total resistance falls, current increases, and therefore the voltage dropped across the fixed resistor increases (as V = IR).
Challenge 3: An automatic street lighting system uses an LDR connected in a potential divider with a 10 kΩ fixed resistor and a 12 V supply. The LDR has a resistance of 50 kΩ in darkness and 1 kΩ in daylight.
(a) Calculate the voltage across the fixed resistor in darkness.
(b) Calculate the voltage across the fixed resistor in daylight.
(c) The light turns on when the voltage across the fixed resistor drops below 1.5 V. Explain whether this system works correctly.
(a) In darkness: R_total = 50 000 + 10 000 = 60 000 Ω. I = 12 ÷ 60 000 = 0.0002 A. V_fixed = 0.0002 × 10 000 = 2 V
(b) In daylight: R_total = 1000 + 10 000 = 11 000 Ω. I = 12 ÷ 11 000 = 0.001 09 A. V_fixed = 0.001 09 × 10 000 ≈ 10.9 V
(c) In darkness the voltage across the fixed resistor is 2 V, which is above the 1.5 V threshold — so the light does NOT turn on in darkness. This system does NOT work correctly as described. (A correction would be to swap the positions of the LDR and fixed resistor, so that the output is taken across the LDR — then the voltage across the LDR would be high in darkness, triggering the light.)
Challenge 4 (Extended): Explain why the resistance of a metal wire increases with temperature, but the resistance of a thermistor (NTC type) decreases with temperature. In your answer, refer to charge carriers and atomic structure. [6 marks]
Metal wire:
• In a metal, the charge carriers are free (delocalised) electrons — these are already present and do not change in number significantly with temperature.
• As temperature increases, the metal ions in the lattice vibrate with greater amplitude.
• These vibrating ions obstruct the flow of electrons more frequently, causing more collisions.
• More collisions = greater impedance to electron flow = higher resistance.
NTC Thermistor (semiconductor):
• A thermistor is made from a semiconductor material (e.g. silicon or germanium).
• At low temperatures, very few electrons have enough energy to break free from their atoms — so there are few charge carriers and resistance is high.
• As temperature increases, more electrons gain enough thermal energy to become free charge carriers.
• The large increase in the number of free charge carriers outweighs the effect of increased lattice vibration.
• More charge carriers = current flows much more easily = resistance decreases significantly.
Summary: In metals, resistance rises with temperature (more ion vibration). In thermistors, resistance falls with temperature (many more charge carriers released).