# Current Division and Voltage Division Rule

## Current Division Rule

A parallel circuit acts as a current divider as the current divides in all the branches in a parallel circuit, and the voltage remains the same across them. The current division rule determines the current across the circuit impedance. The current division is explained with the help of the circuit shown below

The current I has been divided into I_{1 }and I_{2} in two parallel branches with the resistance R_{1 }and R_{2} and V is the voltage drop across the resistance R_{1} and R_{2}.

As we know

V = IR ……..(1)

Then the equation of the current is written as

Let the total resistance of the circuit be R and is given by the equation shown below

Equation (1) can also be written as

I = V/R ……….(3)

Now, putting the value of R from the equation (2) in the equation (3) we will get

Putting the value of V = I_{1}R_{1} from the equation (5) in the equation (4), we finally get the equation as

And now considering V = I_{2}R_{2} the equation will be

Thus, from the equation (6) and (7) the value of the current I_{1} and I_{2} respectively is given by the equation below

Thus, in the current division rule, it is said that the current in any of the parallel branches is equal to the ratio of opposite branch resistance to the total resistance, multiplied by the total current.

## Voltage Division Rule

The voltage division rule can be understood by considering a series circuit shown below. In a series circuit, voltage is divided, whereas the current remains the same.

Let us consider a voltage source E with the resistance r_{1 }and r_{2} connected in series across it.

As we know

I = V/R or we can say I = E/R

Therefore, the current (i) in the loop ABCD will be

By putting the value of i from equation (8) in the equation (9) the voltage across the resistance r_{1 } and r_{2} respectively is given by the equation shown below as

Thus, the voltage across a resistor in a series circuit is equal to the value of that resistor times the total impressed voltage across the series elements divided by the total resistance of the series elements.

## 1 Comment

greatly assisted