Worked example 1

A 12V power supply is connected across two series resistors: R1 = 200Ω and R2 = 400Ω. Calculate the output voltage taken across R2.

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Identify the input voltage: $V_{in} = 12V$ .
Identify the resistances: $R_1 = 200\Omega$ and $R_2 = 400\Omega$ .
Apply the potential divider formula: $V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$ .
Substitute the values: $V_{out} = 12V \times \frac{400\Omega}{200\Omega + 400\Omega}$ .
Calculate the sum of resistances: $V_{out} = 12V \times \frac{400}{600}$ .
Simplify the fraction and calculate: $V_{out} = 12V \times \frac{2}{3} = 8V$ .
The output voltage across R2 is 8V.

Worked example 2

A light-sensing circuit uses a 9.0 V supply, a fixed 10 kΩ resistor, and a Light Dependent Resistor (LDR) in series. The output voltage is taken across the LDR. A switch connected to the output is triggered when the voltage reaches 6.0 V, indicating it is dark. What is the resistance of the LDR at this point?

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Identify known values:
- Input Voltage, $V_{in} = 9.0 \text{ V}$
- Fixed Resistor, $R_1 = 10 \text{ k}\Omega = 10,000 \text{ } \Omega$
- Output Voltage, $V_{out} = 6.0 \text{ V}$
- The output is across the LDR, so $R_2 = R_{LDR}$ .
State the potential divider formula: $V_{out} = V_{in} \times \frac{R_{LDR}}{R_1 + R_{LDR}}$
Rearrange the formula to solve for $R_{LDR}$ :
- Divide by $V_{in}$ : $\frac{V_{out}}{V_{in}} = \frac{R_{LDR}}{R_1 + R_{LDR}}$
- Cross-multiply: $V_{out}(R_1 + R_{LDR}) = V_{in}R_{LDR}$
- Expand the bracket: $V_{out}R_1 + V_{out}R_{LDR} = V_{in}R_{LDR}$
- Group $R_{LDR}$ terms: $V_{out}R_1 = V_{in}R_{LDR} - V_{out}R_{LDR}$
- Factor out $R_{LDR}$ : $V_{out}R_1 = R_{LDR}(V_{in} - V_{out})$
- Isolate $R_{LDR}$ : $R_{LDR} = \frac{V_{out}R_1}{V_{in} - V_{out}}$
Substitute the values and calculate: $R_{LDR} = \frac{6.0 \text{ V} \times 10,000 \text{ } \Omega}{9.0 \text{ V} - 6.0 \text{ V}}$ $R_{LDR} = \frac{60,000}{3.0} \text{ } \Omega$ $R_{LDR} = 20,000 \text{ } \Omega$
Final Answer: The resistance of the LDR is 20 kΩ when the switch is triggered.

Potential dividers — practice questions

Worked example 1

Worked example 2