Potential along a wire and potential dividers

Potential along a uniform wire

When a steady current flows along a uniform resistance wire, the potential falls steadily with distance: equal lengths have equal p.d.s. A graph of potential against distance is a straight line. The p.d. across a length l of a wire of total length L with p.d. V is V x l / L.

The potential divider

Two resistors R1 and R2 in series across an input p.d. V_in share it in the ratio of their resistances. The output across R2 is

V_out = V_in x R2 / (R1 + R2)

The larger resistor gets the larger share of the p.d.

Variable outputs and sensors

• Replace R2 with a variable resistor (or use a potentiometer) to give an adjustable output.
• With a thermistor or LDR, the output changes with temperature or light. Work out which resistance changes, then which share of the p.d. grows.
• Example: LDR as R2, output across it. Brighter light means lower LDR resistance, so V_out falls.

Worked example

A 9.0 V supply is connected across a 2.0 kΩ resistor and a 1.0 kΩ resistor in series. Find the p.d. across the 1.0 kΩ resistor.

1. V_out = 9.0 x 1.0 / (2.0 + 1.0)

Answer: V_out = 3.0 V

Check yourself

1. A 12 V supply is connected across R1 = 4.7 kΩ and R2 = 3.3 kΩ in series. Find the p.d. across R2, in V, to 3 s.f.
   Show answer

   4.95 V. V_out = 12 x 3.3 / 8.0 = 4.95 V.

2. A uniform wire 1.00 m long has 6.0 V across it. Find the p.d. between one end and a point 0.35 m along it, in V.
   Show answer

   2.1 V. The potential falls uniformly: 6.0 x 0.35 / 1.00 = 2.1 V.

3. A potential divider with R1 = 300 Ω must give 2.0 V across R2 from a 5.0 V supply. Find R2 in Ω.
   Show answer

   200 Ω. The p.d. across R1 is 3.0 V. Same current, so R2 / R1 = 2.0 / 3.0, giving R2 = 200 Ω.

4. A thermistor of resistance 2.0 kΩ is in series with a 3.0 kΩ fixed resistor across 6.0 V. Find the p.d. across the fixed resistor, in V.
   Show answer

   3.6 V. V = 6.0 x 3.0 / 5.0 = 3.6 V.

5. An LDR is in series with a fixed resistor. The output is taken across the LDR. The light gets brighter. What happens to the output p.d.?
   • It increases
   • It stays the same
   • It decreases
   • It becomes equal to the supply p.d.
   Show answer

   It decreases. The LDR's resistance falls, so it takes a smaller share of the p.d.

6. An NTC thermistor is in series with a fixed resistor, with the output across the fixed resistor. The temperature rises. What happens to the output?
   • It increases
   • It decreases
   • It stays the same
   • It becomes zero
   Show answer

   It increases. The thermistor's resistance falls, so the fixed resistor takes a larger share of the p.d.

7. How does the potential vary along a uniform wire carrying a steady current?
   • It is the same everywhere
   • It falls quickly at first, then levels off
   • It falls linearly with distance
   • It rises with distance
   Show answer

   It falls linearly with distance. Equal lengths have equal resistance and so equal p.d.s.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.