Potential Divider - a MaS Tutor.

The Potential Divider Equation

$V_{1 or 2} = \frac{V R_{1 or 2}}{R_{1} + R_{2}}$

(both care of byjus.com)

A figure showing a simple potential divider involving two resistances.

For a potential divider the current through each resistance are the same due to Kirchhoff's First Law.

I_{1} = I_{2}

Using Ohm's Law gives

\frac{V_{1}}{R_{1}} = \frac{V_{2}}{R_{2}}

V = V_{1} + V_{2}

Solving these last two equations simultaneously for $V_{1}$ ,

V = V_{1} + \frac{V_{1} R_{2}}{R_{1}}

Simplifying,

V_{1} = \frac{V R_{1}}{R_{1} + R_{2}}

A symmetric argument can be used to show,

V_{2} = \frac{V R_{2}}{R_{1} + R_{2}}