Voltage Division Rule and Current Division Rule

Whenever we apply a voltage across a circuit the circuit divides the voltage according to the distribution of the series impedances in the circuit. Also when we supply an electric current to a circuit the circuit divides the current according to the parallel distribution of the impedances in the circuit. In this article, we are going to discuss the voltage division rule and current division rule one by one.

Voltage Division Rule

Suppose a circuit is having three impedances in series. V is the voltage across the entire circuit. Z1, Z2, and Z3 are the values of the impedances.

series impedances

As the circuit is the series combination of three impedances, the equivalent impedance of the circuit is,

2

Therefore the current through the circuit is

3

Now as per Ohm’s law, the voltage drop across any of the impedances is the product of the current and the value of that impedance. Therefore the voltage drop across Z1 is

4

Then the voltage drop across Z2 is

5

Similarly, the voltage drop across Z3 is

6

From these equations, we can write the expression of the voltage across Z1 as

7

Also, we can write the expression for the voltage across Z2 as

8

Similarly, the expression of the voltage across Z3 is

9

This is how a series circuit divides a voltage according to the value of the impedances.

The same voltage division rule is applicable to the fully resistive circuit. The series combination of resistances divides the voltage according to the value of individual resistances. The voltage division rule is the same but instead of Z we just write R here. We call the series combination of resistances at the voltage divider circuit.

Definition of Voltage Division Rule

The voltage drop across any resistance in a series combination of resistances is the product of the voltage across the entire circuit and the ratio of that resistance to the equivalent resistance of the circuit.

Current Division Rule

A parallel circuit divides current through its parallel branches. The value of the current through each branch is as per the resistive value of the branch. Let us examine the fact. For that, we will draw a circuit with three parallel resistances.

parallel resistances

Let us apply a voltage across the parallel combination of the resistances. The value of the voltage is V. We also consider that the circuit takes current I from the voltage source. Obviously this current gets three parallel paths to flow. Let us assume that the resistance R1 takes the current I1. The resistance R2 takes the current I2. Similarly, the resistance R3 takes the current I3.

So, the voltage drops across R1, R2, and R3 are

11

Since the resistances are in parallel, the voltage drop across each of the resistances is the same and it is equal to the source voltage. Therefore we can write the expression of the currents as,

12

Now as per Ohm’s law the total current entering to the circuit from the source is the source voltage divided by equivalent resistance of the circuit. Therefore we can write

13

So, from the expression of the total current and the current through the individual resistances, we can write

14

Definition of Current Division Rule

In a parallel circuit, the current shared by a branch is inversely proportional to the impedance or resistance of that branch.

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