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Thevenin theorem with example

Short answer

Thevenin's theorem states any linear two-terminal network can be replaced by a voltage source V_th in series with a resistance R_th, where V_th is open-circuit voltage and R_th is equivalent resistance with sources zeroed. It simplifies analysis when load varies, e.g., a network of 24V, 6Ω, 3Ω yields V_th=8V, R_th=2Ω, and load current is V_th/(R_th+RL).

State and explain thevenin's theorem with suitable example.

Statement

Thevenin's theorem: any linear two-terminal network containing sources and resistors can be replaced, as seen from its two terminals, by a single voltage source V_th in series with a resistance R_th.

  • V_th = open-circuit voltage between the terminals (load removed).
  • R_th = resistance between the terminals with all independent sources set to zero (voltage sources shorted, current sources opened).
 Linear network           Thevenin equivalent
 o-------+------o a        o--[R_th]--+------o a
         |                    (V_th)  |  load
 (sources|                            |
  and R) |                            |
 o-------+------o b        o----------+------o b

Steps

  1. Remove the load resistor and mark the two terminals.
  2. Find V_th (open-circuit voltage) by any method.
  3. Set all independent sources to zero and find R_th.
  4. Connect the load to the equivalent: I_L = V_th/(R_th + R_L).

Example

A 24 V source feeds R₁ = 6 Ω in series, with R₂ = 3 Ω across the output terminals, and a load R_L = 4 Ω.

  • V_th = 24 × 3/(6 + 3) = 8 V
  • R_th = 6 ∥ 3 = 2 Ω
  • I_L = 8/(2 + 4) = 1.333 A, V_L = 5.33 V

Check on the original circuit: R_total = 6 + (3 ∥ 4) = 7.714 Ω, I = 3.111 A, and the load receives 3.111 × 3/7 = 1.333 A. The results are the same.

It is useful when one branch (the load) changes while the rest of the network stays the same.

✓ Answer checked by Claude Opus 5.5 (high effort)

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