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## Current Division Rule

When current flows through more than one parallel path, each of the paths shares a definite portion of the total current depending upon the impedance of that path.

The definite portion of the total current shared by any of the parallel paths can easily be calculated if the impedance of that path and the equivalent impedance of the parallel system are known to us.

The rule or formula derived from these known impedances to know the portion of total current through any parallel path is known as the current divider rule. This rule is very important and widely used in the field of electric engineering in different applications.

Actually, this rule finds application when we have to find the current passing through each impedance when these are connected in parallel.

Let us say, two impedances Z_{1} and Z_{2} are connected in parallel as shown below.

A current I passes and is being divided into I_{1} and I_{2} at the junction of these two impedances as shown. I_{1} and I_{2} pass through Z_{1} and Z_{2} respectively. Our aim is to determine I_{1} and I_{2} in terms of I, Z_{1,} and Z_{2}.

As Z_{1} and Z_{2} are connected in parallel, the voltage drop across each will be the same. Hence, we can write

Also applying Kirchoff’s current law at the junction, we get

We have two equations and can determine I_{1} and I_{2}.

From (1), we have

Putting this in (2), we get

or,

or,

or,

We have

Putting the value of I_{1}, we get

Thus, we have determined I_{1} and I_{2} in terms of I, Z_{1,} and Z_{2}.

This rule is applied as follows.

Suppose we have to determine I_{1}. We proceed as

Applying the above rule, we will get

Let us apply this rule to some problems.

Applying the **current division rule**, we will have

Where I_{1} = current passing through Z_{1}.

Putting given numerical values, we get

Similarly,

The other way to find I_{2} is as

This is how we can apply the current division rule.

## Voltage Division Rule

The **voltage division rule** is applied when we have to find the voltage across some impedance. Let us assume that the impedances Z_{1}, Z_{2}, Z_{3},…..Z_{n} are connected in series, and the voltage source (V) is connected across them.

This is shown in the voltage divider circuit below:

Our aim is to find the voltage across some impedance, say, Z_{3}. We see that Z_{1}, Z_{2}, Z_{3} …. Z_{n} are connected in series. Hence, effective impedance Z_{eff} as seen by the voltage is given by

The current passing the circuit is given by

This current is passing through all the impedances connected in series. Hence, the voltage across Z_{3} is given by

Similarly, the voltage across Z_{1} will be given by

In general, we can write

Where, k = 1, 2, 3,….n and impedances Z_{1}, Z_{2}, Z_{3} ,…….Z_{n} should be connected in series.

This is called the **voltage division rule** and frequently used to determine the voltage across some impedance. We can write this rule in words as given below.

The voltage across some impedance

We will solve one problem of finding voltages across impedances using the **voltage division rule**.

### Voltage Division Rule Example Problem

The following impedances are connected in series:

Across this impedance connected in series, a voltage source of 100V is connected as shown below. Determine the voltage across each impedance.

Solution:

Applying the voltage division rule, we get

Similarly,

We can also determine V_{z3} as follows.

Actually, we can determine the voltage across any impedance in this way if voltages across all other remaining impedances are known.

With the impedances equal to:

The voltage across each impedance is given by:

Thus voltage will be the same across each impedance and it equals V/n, that is, source voltage divided by the number of impedances connected in series.