In this article, we will take a look at one of the common circuit analysis theorems the Thevenin theorem.

Thevenin theorem is considered a very effective theorem for solving circuit problems similar to Norton theorem. Using the Thevenin theorem, any circuit can be reduced to Thevenin equivalent circuit.

Table of Contents

## Thevenin theorem statement

**Thevenin’s Theorem:** It states that any linear or bilinear circuit consisting of a voltage source or current source and resistances can be resolved into a circuit with V_{th} (Thevenin equivalent voltage), R_{th} (Thevenin equivalent resistance) & load resistance.

In other words, you can solve any complex linear or bilinear network which consists of several voltage sources or current sources and resistances into the Thevenin equivalent circuit having single voltage source V_{th} (Thevenin equivalent voltage) and single resistance R_{th} (Thevenin equivalent resistance) with the resistance across which you have to find current.

In the fig. 1 circuit on the left-hand side have active and passive components with a load resistor and on the right-hand side, a Thevenin equivalent circuit has equivalent Thevenin voltage connected in series with equivalent Thevenin resistor and load resistor. The value of Thevenin equivalent voltage and Thevenin equivalent resistance are obtained by the Thevenin theorem.

## Steps to solve

- Remove the load resistance R
_{L}or the resistance (if any) from the branch across which you have to obtain current. - Convert voltage source into a short circuit and current source (if any) into an open circuit and then find R
_{th.} - Find V
_{th}by network analysis method. - From step 2 & step 3 you have V
_{th }& R_{th}now find the current flowing through R_{L.}

Now let’s understand the above steps with help of an example.

**Q. Find the current across the 15ohm resistor.**

**Step 1**. Remove the 15ohm resistance.

**Step 2**. In the above fig., we only have a voltage source. So, convert the voltage source with a short circuit. Now let us find the R_{th}

**R _{th }**= r

_{1}+(r2*r3)/r2+r3

= 5+(10*5)/10+5

**R _{th }**=8.33

**Step 3**. Now let us find V_{th.}

Current in the closed-loop,

I = 20/(5+10)

I =1.3

So, the voltage across terminal ab is equal to the voltage drop across the 10ohm resistor.

**V _{th}**= 1.3*10

= 13

**Step 4**. Now we have R_{th} & V_{th}, let’s make Thevenin equivalent circuit and find the current across 15ohm resistor.

**I _{L} **= V

_{th}/R

_{th }+R

_{L}

= 13/8.33+15

=0.55 A

From the above problem you can learn that how to solve a circuit by the Thevenin theorem.