What is voltage divider rule

The voltage divider rule is a simple principle used in electronics to determine the voltage drop across a resistor in a series circuit. In a series circuit, where resistors are connected end-to-end, the total voltage provided by the source is divided among the resistors in proportion to their resistance values.

Key Points

• Formula:
  For two resistors $R_1$ and $R_2$ connected in series with an input voltage $V_{in}$, the voltage across $R_2$ (often taken as the output voltage, $V_{out}$) is given by:

  $$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$$

• General Case:
  For multiple resistors in series, the voltage drop across any resistor $R_i$ is:

  $$V_i = V_{in} \times \frac{R_i}{\sum_{j} R_j}$$

• Usage:
  The voltage divider rule is frequently used in sensor circuits, biasing transistors, and anywhere a specific voltage is needed from a higher-voltage source.

• Assumptions:
  The rule assumes that there is no significant current drawn from the divider (i.e., the load on the voltage divider is very high or is disconnected), so that the current through all resistors remains the same.

Overall, the voltage divider rule is a fundamental tool in circuit analysis, allowing engineers to design circuits that can tap off a specific fraction of an input voltage by appropriately choosing resistor values.