In-circuit analysis the current divider and voltage divider rule is one of the basic rules for easily determining a particular current or voltage across the circuit. Apart from Kirchhoff’s circuit law, this rule is also most commonly used for obtaining current and voltages.

Table of Contents

## Current divider rule

As you know that in parallel circuits the current divides across branches but the voltage remains the same across the branches. Let’s consider a circuit. In the fig. below the current, I divides into two parts I_{1} & I_{2} across the resistance R_{1} & R_{2} but the voltage V remains the same across both the resistors.

So, as the ohm’s law is V = I*R or I = V/R** **…………….. Eq.1

So, I_{1} = V/R_{1} & I_{2} = V/R_{2} ……………….. Eq.2

Let the total resistance of the circuit is

R = R_{1}*R_{2} / (R_{1}+R_{2}) ………… Eq.3

Put the value of R in eq.1

I = V*(R_{1}+R_{2}) / R_{1}*R_{2} ……………. Eq.4

Now as V = I_{1}*R_{1} & V = I_{2}*R_{2} ……………. Eq.5

Putting Eq.5 in Eq.4

I = I_{1}*R_{1 }*(R_{1 }+ R_{2 })/ R_{1} R_{2 } _{ }and I = I_{2}*R_{2 }*(R_{1 }+ R_{2 })/ R_{1} R_{2 }

Therefore,

I_{1 } = I*R_{2 }/R_{1}+R_{2}

I_{2 } = I*R_{1 }/R_{1}+R_{2}

## Voltage divider rule:

As in parallel circuits, current divides between two branches similarly in series circuit voltage divides across each resistor and the current remains the same. In the fig. below total voltage is divided across every resistor and the current is the same across these resistors.

V = I*R (Ohm’s law)

So, V_{1 }= I*R_{1 }……………. Eq.6

I = V/R_{total } i.e. I = V/R_{1}+R_{2}+…..+ R_{n }

Putting the value of I in Eq.6

V_{1} = V*R_{1}/R_{1}+R_{2}+…..+ R_{n }

V_{2} = V*R_{2}/R_{1}+R_{2}+…..+ R_{n } ** **

V_{n} = V*R_{n}/R_{1}+R_{2}+…..+ R_{n } ** **