Voltage Divider Rule

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It can be quite useful to determine how a voltage appearing across two series resistors “divides” between them.

Consider the circuit shown below:

Voltage Divider Rule

By Ohm’s Law, the current in the resistors is:

current in the resistors

By application of Ohm’s Law again, the voltage across R1  is:

v1 = R1 . i

and therefore:

Voltage divider rule formula

Similarly, the voltage across R2  is:

Voltage divider rule formula 2

These equations describe how the voltage is divided between the resistors. Because of this, a pair of resistors in series is often called a voltage divider.

Example:

We want to find the voltage v in the circuit below:

Voltage Divider Rule Circuit Example

Combining the series connection of the 1 ohm and 3 ohm resistors, we obtain the

Voltage Divider Rule Circuit Example 1

Now the pair of 4 ohms resistors in parallel can be combined as shown below:

Voltage Divider Rule Circuit Example 2

By voltage division:

Voltage Divider Rule Circuit Equation

Returning to the original circuit and applying voltage division again yields:

Voltage Divider Rule Circuit Equation 1

Engineering Tutorial Keywords:

  • the formula of current divider when series-parallel circuit
  • voltage divider example
  • voltage divider rule yields
  • voltage divider through a resistor

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