gen-define-the-voltage-divider-and-give-one-short-worked-example-2d11

Define the voltage divider and give one short worked example.

# Voltage Divider ## Definition A **voltage divider** is a circuit that produces an output voltage that is a fraction of its input voltage. It consists of two or more resistors in series, where the output voltage is taken across one of the resistors. ## Formula For two resistors in series: $$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$$ where: - $V_{in}$ = input voltage - $V_{out}$ = output voltage across $R_2$ - $R_1$, $R_2$ = resistances in the divider ## Worked Example **Problem:** A 12V battery is connected to a voltage divider with $R_1 = 3\text{kΩ}$ and $R_2 = 1\text{kΩ}$. Find $V_{out}$ across $R_2$. **Solution:** $$V_{out} = 12V \times \frac{1\text{kΩ}}{3\text{kΩ} + 1\text{kΩ}} = 12V \times \frac{1}{4} = 3V$$ The output voltage is **3V**.