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:


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

v1 = R1 . i

and therefore:


Similarly, the voltage across R2  is:


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.


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


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


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


By voltage division:


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


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Voltage Divider Rule

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