13 Jun 2026

Verification of Thevenin's and Norton's Theorems

practical pg-iv electronics network-analysis thevenin norton

Aim

To verify Thevenin’s and Norton’s theorems for a linear DC resistive network.

Apparatus

DC supply, resistors, load resistor, voltmeter, ammeter, potentiometer or decade resistance box, and connecting leads.

Experimental arrangement

The original network is replaced by its equivalent source and resistance, and the load current is compared in all arrangements.

Theory

A linear resistive network responds to a load through the voltage and current available at its two output terminals. To find its Thevenin form, remove the load and measure the open-circuit terminal voltage $V_{th}$; then deactivate independent sources and measure the resistance seen from the terminals, $R_{th}$. Thevenin’s theorem replaces the network by $V_{th}$ in series with $R_{th}$.

Norton’s theorem follows from the same terminal relation. Measure the short-circuit current $I_N$, and place it in parallel with $R_N$. The two forms satisfy $V_{th}=I_NR_N$ and $R_{th}=R_N$. For a load $R_L$,

\[I_L=\frac{V_{th}}{R_{th}+R_L}=I_N\frac{R_N}{R_N+R_L}.\]

The theorem is verified when the load current obtained from the original and equivalent circuits agrees within the experimental error.

Observations

Arrangement	Load resistance (ohm)	Load current (mA)
original network	1000	3.96
Thevenin equivalent	1000	3.94
Norton equivalent	1000	3.95

Calculation

For the trial network take the measured Thevenin parameters as $V_{th}=5.00$ V and $R_{th}=260\,\Omega$. The predicted load current for $R_L=1000\,\Omega$ is

\[I_L=\frac{V_{th}}{R_{th}+R_L}=\frac{5.00}{260+1000}=3.968\times10^{-3}\,\text{A}=3.97\,\text{mA}.\]

The equivalent Norton current is

\[I_N=\frac{V_{th}}{R_{th}}=\frac{5.00}{260}=19.23\,\text{mA},\qquad R_N=R_{th}=260\,\Omega.\]

Using the Norton form gives

\[I_L=I_N\frac{R_N}{R_N+R_L}=19.23\frac{260}{1260}=3.97\,\text{mA}.\]

The observed currents, 3.96, 3.94, and 3.95 mA, differ from this ideal value by less than one percent.

Result

The load currents in the original, Thevenin-equivalent, and Norton-equivalent circuits agree within experimental error.

Viva Questions

1. What is $V_{th}$? The open-circuit voltage at the output terminals.
2. How is $R_{th}$ found? Deactivate independent sources and find the resistance seen from the terminals.
3. What is the Norton current? The short-circuit current at the output terminals.

Maxima Code

Download the Thevenin-Norton calculation.