Network Reduction and Theorems for dc and ac Circuits

Unit - II

NETWORK REDUCTION AND THEOREMS FOR DC AND AC CIRCUITS

VOLTAGE DIVISION:

To find the expressions for the voltages V₁, V₂ and V3 in terms of V, R₁, R₂, R₃ for

Current division formula:

(a) In many cases, we will have only two resistors connected in parallel

Let these resistors be R₁ and R₂ as shown in the Fig.2.2.

The total current = I

Current through R₁ = I

Current through R₂ = I₂

To express I₁, and I₂, in terms of I, R₁ and R₂.

Note: In case R, and R2 are parallel, the equivalent resistance R can be found as below: We come across parallel combination of two resistors very often. So it is better to remember the following formula for R.

The reader is to note that the above formula is true only for two resistances in parallel.

(b) When three resistors are in parallel: To find equivalent resistance and the expressions for branch currents. Refer Fig.1.12

Let R₁, R₂ and R₃ be the resistors in parallel.

Let I be the supply current or total current.

Let I₁, I₂ and I₃ be the currents through R₁, R₂ and R₃ respectively.

To find the currents I₁, 1₂ and 1₃ : Given R₁, R₂, R₃ and I.

We know that,

Note:

1. If there are n resistors each of R ohms connected in parallel, the equivalent resistance is R_T = R / n

2. For getting more resistance we need series combination.

3. For getting lesser resistance we need parallel combination.