13 Jul 2026

Verification of Thevenin, Norton, Superposition and Maximum Power Transfer Theorems

practical ug-iv electronics network-theorems

Experimental arrangement

DC network test circuit with a source, series limiting resistance, network under test, and separate current and voltage readings.

Aim

To verify Thevenin’s theorem, Norton’s theorem, the superposition theorem, and the maximum power transfer theorem for a DC resistive network.

Apparatus

DC power supplies, resistors, rheostat, voltmeter, ammeter, resistance box, key, and connecting wires.

Theory

Thevenin’s theorem replaces a linear two-terminal network by an equivalent voltage source $V_{th}$ in series with $R_{th}$. Norton’s theorem replaces it by a current source $I_N$ in parallel with $R_N$, where $R_N=R_{th}$. In the superposition theorem, the response in a linear network is the algebraic sum of responses produced by individual sources acting separately. Maximum power is delivered to the load when

\[R_L=R_{th}.\]

Observations

Thevenin and Norton check

Quantity	Direct network	Equivalent network
Open-circuit voltage $V_{th}$	$6.02\,\text{V}$	$6.00\,\text{V}$
Short-circuit current $I_N$	$12.0\,\text{mA}$	$12.1\,\text{mA}$
Equivalent resistance	$500\,\Omega$	$495\,\Omega$

Superposition check

Response	Measured current
Source $E_1$ alone	$4.0\,\text{mA}$
Source $E_2$ alone	$2.0\,\text{mA}$
Both sources together	$6.0\,\text{mA}$

Maximum power transfer

$R_L$ ($\Omega$)	Load power (mW)
250	16.0
400	18.4
500	18.0
600	17.1
1000	12.0

Result

The measured equivalent voltage, equivalent resistance, and source superposition agree with the corresponding theoretical values within experimental error. Maximum load power occurs close to $R_L=R_{th}$.

Precautions

1. Switch off the supply while changing the circuit.
2. Check meter polarity and range before taking readings.
3. Replace an ideal voltage source by a short circuit only when finding equivalent resistance.
4. Use a low resistance range for continuity checks and never short a powered supply.

Viva Questions

1. When is Thevenin’s theorem applicable? To linear two-terminal networks.
2. What is the relation between Norton and Thevenin resistance? $R_N=R_{th}$.
3. How is an inactive voltage source replaced? By a short circuit.
4. When is maximum power transferred? When the load resistance equals the Thevenin resistance.
5. Why is superposition not applied directly to power? Power is proportional to the square of current or voltage and is therefore not a linear quantity.