Voltage Divider Rule

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

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Voltage Divider Rule

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