Potential Dividers — Quick Summary

Mr Toogood's Physics · Electricity basics

AQA 3.5.1.5
V_out=V_in×R₁/(R₁+R₂)
Divider equation
I = V/R_T
Alt. method: current
V = IR₁
Alt. method: p.d.
LDR: R↓ as light↑
Sensing component

Potential divider basics

The emf of a supply is shared between series resistors in proportion to their resistance. A potential divider uses this to "tap off" a chosen fraction of the supply voltage.

Two basic potential divider circuits: fixed and variable resistor pair, and a tapped potentiometer

Two forms: fixed+variable resistor pair, or a tapped potentiometer/rheostat.

  • Resistor pair: increasing the variable resistor increases the p.d. across it (and the voltmeter reading).
  • Potentiometer/rheostat: moving the slider continuously changes the tapped-off voltage.

The potential divider equation

Labelled potential divider circuit anchoring the divider equation

V_out is taken across R₁ in this labelling.

V_out = V_in × R₁/(R₁+R₂)
Not on the equation sheet — worth memorising. Alternative: find I=V_in/R_T, then V=IR₁.

Sensing circuits: LDR & thermistor

LDR used in a potential divider circuit to create a light-sensing circuit

LDR in a divider: output p.d. responds to light intensity.

Replace a fixed/variable resistor with an LDR (resistance falls as light increases) or an NTC thermistor (resistance falls as temperature increases) to build a sensing circuit.

Position matters: swapping which resistor is the LDR/thermistor flips the response. If it's the component whose p.d. you're reading, more light/heat → lower resistance → lower p.d. there (and vice versa for the other resistor).

Stabilising a varying supply

If the supply itself fluctuates (e.g. a solar cell), a potential divider can be designed so the p.d. across the output stays roughly constant, keeping downstream circuitry powered reliably.

Exam essentials

Key equation & method

  • V_out=V_in×R₁/(R₁+R₂) — check which resistor is on top.
  • Alt. route: I=V_in/R_T, then V=IR for the resistor you want.

Sensing logic

  • LDR: R decreases as light increases.
  • NTC thermistor: R decreases as temperature increases.
  • Always trace which component's p.d. you're asked about before deciding "rises" or "falls."

Common slips

  • Mixing up R₁ and R₂ in the ratio — the numerator must match the resistor you want V across.
  • Keep all resistances in the same units (e.g. all kΩ) before adding.
  • Round only the final answer — keep full precision through intermediate steps.