# Potential Divider Formula Derivation

Potential divider
*formula derivation*, also known as the potential divider law, is very simple and here are the steps that you can follow easily to derive it.
Ohm’s Law is utilised everywhere in this proof so please make sure you are familiar with that first.

Vs = I × Rtot

However, we know that Rtot = R1 + R2 so we substitute this into the equation above to give the following expression.

Vs = I × (R1 + R2)

The above expression transposes to give the following expression for current.

I = Vs / (R1 + R2)

We know that the following expression for the output voltage is true.

Vo = I × R2

Substituting the previous expression for current into the above equation, we get the following.

Vo = Vs × R2 / (R1 + R2)

## Voltage Divider Rule

The voltage divider rule is very simple and shows that the output voltage Vo is a fraction of the input voltage Vs, and the voltages across the resistors divide in ratio to their values. The following ratio gives the output voltage across R2.

R2 / (R1 + R2)

Therefore, a product of this ratio with the input voltage Vs gives the output voltage across the resistor R2.

Therefore, the following ratio may be utilised to give the voltage across R1.

R1 / (R1 + R2)

Therefore, as you can see, the rule may be utilised for any number of resistors.

## When R1 = R2

The R1 = R2 condition is when the resistors are equal in value. This should provide us with the midpoint, which is exactly half of the input supply voltage.

Vo = Vs × R2 / (R1 + R2)

Substituting for R1 in the above formula, we get the following.

Vo = Vs × R2 / (R2 + R2)

The above expression simplifies since the R2 values add to give 2 × R2

Vo = Vs × R2 / 2 × R2

The above expression simplifies further since R2 above the numerator and denominator cancels, to give the following result.

Vo = Vs / 2

## Rearranging the Potential Divider Formula

By rearranging the formula, you can obtain the transfer function given by the ratio Vo and Vs in terms of the resistors R1 and R2.

Vo = Vs × R2 / (R1 + R2)

Dividing by Vs on both sides of the equation cancels out the Vs term on the RHS, thus providing the following expression.

Vo / Vs = R2 / (R1 + R2)

## This Article Continues...

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