3.5.1.5
Potential divider
Circuits & Potential Dividers — AQA A-Level Physics
Key Definition
Potential divider — A circuit of two or more resistors in series used to produce an output p.d. that is a fraction of the input p.d.
$$V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}$$
- Two resistors in series with a supply voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. V_in.
- The output p.d. V_out is taken across one of the resistors.
- V_out depends on the ratio of the resistances.
$$V_{\text{out}} = \frac{R_2}{R_1 + R_2} \, V_{\text{in}}$$
- The ratio of p.d.s equals the ratio of resistances.
- If R_2 increases, V_out increases.
- If R_1 increases, V_out decreases.
$$\frac{V_{\text{out}}}{V_{\text{in}}} = \frac{R_2}{R_1 + R_2}$$
Worked Example
A 12 V supply is connected across a potential dividerA circuit that uses two or more resistors in series to produce a fraction of the source voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. across one of the resistors. with R_1 = 400 ohm and R_2 = 200 ohm. Calculate V_out across R_2.
Show Solution
1
$V_out = R_2 / (R_1 + R_2) \times\;\text{V}_in.$
2
$V_out = 200 / (400 + 200) \times 12.$
3
$V_out = 200/600 \times 12 = 4.0\;\text{V}.$
Answer
4.0 V
Simple potential dividerA circuit that uses two or more resistors in series to produce a fraction of the source voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. across one of the resistors. circuit
V_in across R_1 and R_2 in series. V_out taken across R_2. An output terminal pair shown.
Common Mistake
MEDIUM
Students often: Using the wrong resistor in the numerator. Writing R_1 instead of R_2 when V_out is across R_2.
Instead: The resistor in the numerator is always the one you are measuring V_out across.
Instead: The resistor in the numerator is always the one you are measuring V_out across.
Examiner Tips and Tricks
- Do a sense check: V_out must be less than V_in.
- If your answer is larger, you have swapped R_1 and R_2.