*The Thevenin theorem helps us to reduce the complex electrical circuits to a single voltage source and a single resistance.***Many times the electrical circuits contain multiple current and voltage sources with different components. The behavior of voltage versus resistance for such circuits can be easily performed using the Thevenin theorem. Consider a design engineer who analyzes different mobile phone chargers. For designing the chargers he wants to observe the voltage versus resistive behavior at output terminals. An easy approach for starting the analysis is to reduce the entire circuit to a single voltage source via the Thevenin Theorem.**

Steps which should be followed to reduce a circuit to

**Thevenin equivalent circuit.**
Step 1: Replace the load resistor (if any) and label the leftover terminals.

Step 2: Replace the current and voltage source in the circuit. A current source is replaced by an open circuit and a voltage source is replaced by a short circuit.

Step 3: Find the equivalent resistance of new circuit from the end terminals. This equivalent resistance is the thevenin equivalent resistance.

Step 4: Find the output voltage at load terminals, this voltage is the Thevenin voltage source which joins resistor in series. Application of Superposition theorem comes handy in solving the step 4.

Step 5: Connect the votlage source with resistor to form the final Thevenin equivalent circuit.

### Example of Thevenin Theorem

Let's consider a circuit which has two sources, two resistors and a potentiometer connected as load:

Step 1: To replace the source and naming the leftover terminals.

Step 2 & Step 3: Replace the current source by an open circuit and voltage source by a short circuit and find the equivalent resistance across the terminals a and b.

Step 4: The output voltage across terminal 'ab' is the sum of voltage provided by 10 V source and the voltage provided by the 2.5 mA current source. The application of superposition principle provides an easy way to solve both sources individually and then adding their effect.

You can learn the Superposition theorem here.

Let's first consider the voltage source. The new circuit after replacing current source is a voltage divider:

As you see, the voltage source contributes a 3.33 V thevenin voltage.

The contribution of current source in Theving voltage can't be calculated directly. An alternative solution is to first apply the current divider for finding current across 2.5 ohm resistor and then use the Ohm's law for finding voltage across it.

From Ohm's law:

V_1 = 1.66 * 2.5 = 4.15V

Finally both voltages are added (polarities are same) to acheive an equivalen thevenin source:

V_th = 3.33 V + 4.15 V = 7.48 V

Step 5: Finally the 7.48 V connects in series with 1.667 ohms resistor to find the final circuit. Now we can easily use the Ohm's law performing analysis on the current which was not possible in the previous case.

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