Potential Divider

A potential divider is a simple circuit that splits a battery’s voltage between two (or more) resistors in series. It gives a chosen fraction of the supply voltage for use by another part of a circuit, such as a sensor, dimmer, or volume control.

Key idea

In series, the current is the same through each component. The potential difference (p.d.) across a resistor is given by $V = I R$. If the current is constant, a bigger resistance gets a bigger share of the p.d. The total p.d. is shared between the resistors and equals the supply voltage.

Two-resistor divider formula

With resistors $R_1$ and $R_2$ in series across a supply $V_{\text{s}}$, the p.d. across each is:

Ratio form: $\dfrac{V_1}{V_2} = \dfrac{R_1}{R_2}$

Direct form (useful for outputs):

$$V_1 = V_{\text{s}} \times \frac{R_1}{R_1 + R_2}, \qquad V_2 = V_{\text{s}} \times \frac{R_2}{R_1 + R_2}$$

Variable potential divider (potentiometer)

A variable potential divider uses a resistor with a sliding contact (a potentiometer). Moving the slider changes $R_1$ and $R_2$, so the output p.d. changes smoothly from 0 V up to the supply voltage. This is used in dimmer switches and volume controls.

Using sensors

• LDR (light-dependent resistor): resistance decreases in bright light. Place the LDR as $R_1$ or $R_2$ to make the output increase or decrease with light as needed.
• Thermistor (NTC): resistance decreases when temperature increases. Use the same idea to make temperature control circuits.

Common mistakes

• Thinking each resistor “gets” the same voltage. In series, voltage shares in proportion to resistance.
• Forgetting that the current is the same through series resistors.
• Mixing up which resistor the output is taken across. Always label $R_1$, $R_2$, and where $V_\text{out}$ is measured.