**The Thevenin theorem** is a theorem use to change the complex electrical network into a simple electrical network consisting single resistance in series with load resistance. In most of electrical network to find out the current and voltage in any branch or circuit we use Ohm’s law, Kirchhoff’s voltage and Kirchhoff’s current law to solve the complex circuit, but you must know there are many circuit theorem to analysis the circuit current and voltage at any given point or branch. The Thevenin theorem is mostly use in place of various circuit theorems. In this tutorial we are going to understand about Thevenin’s theorem with solve example in detail.

## What is Thevenin’s Theorem (Thevenin’s Equivalent)?

The thevenin’s theorem states that “Any liner network consisting several voltages and resistances can be replace by a single equivalent voltage in series with a single resistance connected to load in series combination”. In other word the thevenin theorem are simplify any complex network, to replace by simple equivalent two terminal voltage just by single voltage and equivalent single resistor in series with load. The thervenin’s complex and equivalent circuit bock diagram are shown below:-

This theorem is also applicable for analysis of power, but in superposition theorem power cant analysis through it except, three exceptions that exception are given below:-

- Sinusoidal source have different frequency on the network.
- Two sinusoidal sources have same frequency but phase difference is 90 degree operating on network.
- In DC network, power is individual sum.

**Thevenin’s theorem statement**

“In any liner complex network is equivalent to one voltage in series with a single resistance connected to load in series combination”.

### Thevenin equivalent circuit

In thevenin’s circuit the load resistance R_{L} is concerned, in any complex “one-port” network consisting a multiple voltage and resistance element can be replace by single equivalent R_{s} and single equivalent voltage source V_{s}. R_{s} is the source resistance value looking back into the circuit and V_{s} is the open circuit voltage at the terminals.

### Thevenin’ Theorem Example

Let us understand the thevenin’s theorem with an example

**Example: **find out the thevenin voltage and resistance. the circuit diagram are shown below.

**Step 1: **The analysis of the above circuit diagram using Thevenin’s theorem, firstly we remove the load resistance, in this case, 40 Ω.

**Step 2: **Remove all voltage sources internal resistance by shorting all the voltage sources connected to the circuit, i.e. v = 0. If any current sources are present in circuit, then remove the internal resistance by open circuiting the sources.

**Step 3: **Find the value of equivalent resistance, Rs is found by calculating the total resistance looking back from the terminals A and B with all the voltage sources shorted and the load resistance removed. We then get the following circuit.

Find the Equivalent Resistance (Rs)

** **

**Step 4: **Find the equivalent voltage.

To calculate the equivalent voltage source, We now need to reconnect the two voltages back into the circuit, and as V_{S} = V_{AB} the current flowing around the loop is calculated as:

This current of 0.33 amperes (330mA) is same for 20Ω resistor or the 10Ω resistor and it is determine by as follow:

V_{AB} = 20 – (20Ω x 0.33amps) = 13.33 volts.

or

V_{AB} = 10 + (10Ω x 0.33amps) = 13.33 volts, the same.

**Step 5: **Draw the Thevenin’s equivalent circuit. The Thevenin’s equivalent circuit element will be 6.67 Ω series resistance and a 6.67 Ω voltage source. In below circuit diagram show it.

The current flowing in the above circuit will be calculated as:

In an AC and DC circuit the thevenin’s theorem can be apply. But it should be a liner circuit.

## Thevenin’s Theorem Solved Example

Find out the* thevenin voltage (V _{TH}), thevenin resistance (R_{TH}*

*)*and the load current

*I*flowing through and load voltage, Using thevenin’s theorem. The circuit diagram are shown below.

_{L}**Solution:**

**Step 1: **firstly we remove the load resistance 5 kΩ from the circuit.

**Step 2: **calculate the open-circuit voltage. This open circuit voltage wills you the Thevenin’s voltage (V_{TH}).

**Step 3: **find out the current that follow thought resistor 12 kΩ and 4 kΩ resistors by applying current division rule.

**I = 48 V /( 12 kΩ + 4 kΩ) = 3 mA**

The voltage across the 4 kΩ resistors will be:

= 3 mA x 4 kΩ = 12 V

There is no current follow through 8 kΩ resistor, so there is no voltage drop across it and hence the voltage across the terminals AB is same as the voltage across the 4 kΩ resistor. Therefore, AB terminal voltage is12 V. Hence, the Thevenin’s voltage, V_{TH} = 12 V.

**Step 4: **now we calculate the thevenin resistor across the AB terminal.

**From figure, **the 8 kΩ resistor is in series with the parallel connection of 12 kΩ and 4 kΩ resistors. So thevenin resistor will be calculated as follow:

8kΩ + (4k Ω || 12kΩ)

R_{TH} = 8 kΩ + [(4 kΩ x 12 kΩ) / (4 kΩ + 12 kΩ)]

R_{TH }= 8 kΩ + 3 kΩ

R_{TH} = 11 kΩ

**Step 6: **Now, from a new circuit diagram by connect the** **R_{TH} in series with Voltage Source V_{TH} and the load resistor.

**Step 7: the final stage is to calculate the voltage and current across the load by using Ohm’s law as follow:** I_{L} = V_{TH} / (R_{TH} + R_{L})

I_{L} = 12 V / (11 kΩ + 5 kΩ) = 12 V/16 kΩ = 0.75 mA

The load voltage is determined as follows:

V_{L} = 0.75 mA x 5 kΩ = 3.75 V

### Thevenin Theorem Applications

- It is use for analysis of power systems.
- It is used to measurement resistance using the Wheatstone bridge and source modeling.

### Thevenin Theorem Limitations

- It is only applicable for liner circuit.
- The power dissipation applicable for calculating power dissipation.

**Frequenty ask question **

**What is Thevenin’s theorem formula?**

The thenenin voltage or open circuit voltage is **V _{Th}=V_{oc} **across the load terminal. The thenenin voltage formula is:

**I=V _{th}/R_{th}**

**+R**

_{L}**What is basic difference between Norton’s theorem and Thevenin’s theorem?**

The basic difference between thenenin and Norton is – the Norton’s theorem is using for a current source, whereas Thevenin’s theorem uses a voltage source. In thevenin’s theorem the thevenin resistor in series with load but in Norton’s theorem is the resistor is use in parallel with load.

**What is Thevenin’s theorem used for?**

By using thevenin’s theorem any liner complex circuit is transfer into a simple circuit, which typically has a load that changes value during the analysis process.

**What are the limitations of Thevenin theorem?**

Limitations of Thevinen’s Theorem

**it is not applicable for non linear elements, **also to the unilateral networks it is not applicable. There should not be magnetic coupling between the load and circuit to be replaced with the thevinen’s equivalent.

**What is Z in Thevenin’s theorem?**

The Thevenin impedance is the impedance that is to be calculated by short circuit voltage source and open circuit for current source. Z_{Th} = **ohms at degrees**.

**What is relationship between Thevenin and Norton Theorem?**

Thevenin and Norton’s are dual. The Norton’s theorem is the current source transformation of thevenin’s volage. The resistor of both theorems is same. The thevenin voltage is equal to the multiplication of Norton current and Norton resistance. And Norton current is equal to Thevenin.

**What is Thevenin’s resistance?**

The thenenin resistor is the part of thevenin’s theorem. The thevenin resistor is calculated by short circuit the voltage and open circuit for currant. Look the all series and parallel resistor in front from load.

**What is Thevenin’s voltage Vth?**

The thevenin voltage is to be calculated across the load using Kirchhoff’s law. And that voltage will be Thevenin’s voltage Vth.