### Thevenin’s theorem Definition

In any linear bi-directional circuit having more number of elements, it can be replaced by a single equivalent circuit consisting of equivalent voltage (Thevenin equivalent voltage) in series with an equivalent resistance (Thevenin equivalent resistance).

By using Thevenin’s theorem load current can be calculated either in linear or nonlinear load. Consider a circuit as shown below.

**Thevenin Equivalent voltage**

The voltage across the terminals a-b when they are open circuited. It is denoted by V_{th}.

**Thevenin Equivalent Resistance**

It is the ratio of the open-circuit voltage & the short-circuit current at the terminals a-b of the original network. It is denoted by R_{th}.

The Thevenin equivalent circuit is shown below.

### How to solve problems using Thevenin theorem

- Firstly open circuit the terminals a-b (across which you want to find current or voltage)
- Next, Find the open circuit voltage V
_{oc}across the terminals a-b using superposition, KCL, KVL or node and mesh theorems. - Next, find the short circuit current I
_{sc}through the terminals a-b by short-circuiting terminals a & b. - Calculate Thevenin equivalent resistance R
_{th }using R_{th}= V_{oc}/I_{sc} - Draw the Thevenin equivalent circuit between the Thevenin terminals a-b by connecting the voltage source V
_{th}in series with R_{th}. - The external circuitry that was removed in step-1 is now connected across the Thevenin terminals a-b.

**Excercise**

**Q. What is the utility of Thevenin theorem?**

**Ans.** This theorem is useful when we are to determine the current in a particular element of a linear bilateral network particularly when it is desired to find the current which flows through a resistor for its different values. It makes the solution of the complicated circuits quite simple.