Object:

To verify Thevenin’s theorem by replacing a linear DC network with an equivalent voltage source Vth in series with an equivalent resistance Rth, and comparing the load voltage and current.

Apparatus Required:

12 V regulated DC supply, 1 kΩ resistor, 2.2 kΩ resistor, load resistors of 470 Ω, 1 kΩ and 2.2 kΩ, digital multimeter, breadboard/trainer board and connecting wires.

Theory:

Thevenin’s theorem states that any linear, bilateral two-terminal network containing sources and resistances can be replaced at its output terminals by one ideal voltage source Vth in series with an equivalent resistance Rth. Vth is the open-circuit voltage across terminals A–B with RL removed. To find Rth, deactivate independent sources: replace an ideal voltage source with a short circuit and an ideal current source with an open circuit. For a load RL, IL = Vth/(Rth + RL) and VL = IL × RL.

Circuit Diagram:

Left: original circuit. Right: Thevenin equivalent seen from terminals A–B. Remove RL to measure Vth. For Rth, turn off the 12 V ideal source (short it) and look into terminals A–B.

Circuit Values and Calculations:

Given: Vs = 12 V, R1 = 1 kΩ, R2 = 2.2 kΩ.

Vth = Vs × R2/(R1 + R2) = 12 × 2.2/(1 + 2.2) = 8.25 V.

Rth = R1 || R2 = (1000 × 2200)/(1000 + 2200) = 687.5 Ω.

For RL = 1 kΩ: IL = 8.25/(687.5 + 1000) = 4.89 mA; VL = IL × RL ≈ 4.89 V.

Procedure:

1. Connect the original circuit as shown, leaving RL disconnected. Set the DC supply to 12 V.

2. Measure the voltage across A–B with RL removed. Record this open-circuit voltage as measured Vth.

3. Switch OFF and disconnect the supply. Replace the ideal voltage source by a short circuit; measure resistance looking into A–B to obtain Rth. Never use an ohmmeter on an energized circuit.

4. Reconnect the original circuit and connect RL = 470 Ω. Measure VL across RL; determine IL from IL = VL/RL or measure current in series.

5. Repeat for RL = 1 kΩ and 2.2 kΩ.

6. Calculate the expected VL and IL using the Thevenin equivalent and compare with the original-circuit readings.

7. Switch OFF the supply and disconnect the circuit.

Observation Tables:

Table A: Determination of Vth and Rth

Quantity	Calculated value	Measured value	Unit
Open-circuit voltage, Vth	8.25	________	V
Thevenin resistance, Rth	687.5	________	Ω

Table B: Load verification readings (calculated reference values)

RL (Ω)	Original VL (V)	Original IL (mA)	Thevenin VL (V)*	Thevenin IL (mA)*	% difference
470	3.35	7.13	3.35	7.13	________
1000	4.89	4.89	4.89	4.89	________
2200	6.29	2.86	6.29	2.86	________

Sample Expected Readings:

RL = 470 Ω: Original network VL ≈ 3.35 V, IL ≈ 7.13 mA; Thevenin network VL ≈ 3.35 V, IL ≈ 7.13 mA.

RL = 1000 Ω: Original network VL ≈ 4.89 V, IL ≈ 4.89 mA; Thevenin network VL ≈ 4.89 V, IL ≈ 4.89 mA.

RL = 2200 Ω: Original network VL ≈ 6.29 V, IL ≈ 2.86 mA; Thevenin network VL ≈ 6.29 V, IL ≈ 2.86 mA.

Result:

Thevenin’s theorem is verified if the load voltage and current in the original circuit are approximately equal to those in the Thevenin-equivalent circuit, within component and instrument tolerances.

Precautions:

• Keep the supply OFF while wiring or changing components.

• Check resistor values and supply polarity before switching ON.

• Measure voltage in parallel and current in series; alternatively calculate IL = VL/RL.

• Never measure resistance in an energized circuit.

• Use a suitable meter range and avoid shorting the supply.

• Enter actual measurements honestly; do not label theoretical values as measured values.

Viva-Voce Questions:

1. State Thevenin’s theorem.

2. How is Vth determined?

3. How is Rth found when only an ideal voltage source is present?

4. Why is the load removed while measuring Vth?

5. Can Thevenin’s theorem be directly applied to a nonlinear network?

6. Write the expression for load current using Vth, Rth and RL.

7. Why may practical readings differ from calculated readings?