Object:

To verify the Maximum Power Transfer Theorem by varying the load resistance and observing the power delivered to the load.

Apparatus Required:

Regulated DC power supply (12 V), resistors (1 kΩ and suitable load-resistance decade box or resistors), digital multimeter(s), breadboard/trainer board, connecting wires.

Theory:

The Maximum Power Transfer Theorem states that a linear DC network delivers maximum power to a load when the load resistance equals the Thevenin resistance of the network as seen from the load terminals: RL = Rth. For a Thevenin source Vth in series with Rth, load current IL = Vth/(Rth + RL), load voltage VL = IL × RL, and load power PL = VL²/RL = IL²RL.

For AC networks, maximum average power transfer occurs when the load impedance is the complex conjugate of the Thevenin impedance. This experiment uses a resistive DC circuit.

Circuit Diagram:

Use a 12 V DC source with a 1 kΩ series resistance and vary RL. The load voltage is measured across RL; load current may be measured in series or calculated from VL/RL.

Thevenin Equivalent:

For this circuit, Vth = 12 V and Rth = 1 kΩ. Therefore, maximum power is expected when RL = 1 kΩ.

Procedure:

Keep the DC supply OFF while making connections. Assemble the circuit as shown in the diagram.
Set the regulated DC supply to 12 V and verify the polarity before switching it ON.
Set the load resistance RL to 500 Ω. Measure and record the voltage VL across the load.
Repeat the measurement for each RL value listed in the observation table.
For each reading, calculate IL = VL/RL and PL = VL²/RL. If current is measured directly, record it and use it to calculate PL = IL²RL.
Compare the calculated load power for all load resistances and identify the resistance at which power is maximum.
Switch OFF the supply before changing circuit connections.

Observation Table:

Supply voltage Vs = 12 V; series resistance Rs = 1 kΩ. The table below contains theoretical/expected values for guidance, not actual laboratory measurements.

S. No.	Load RL (Ω)	Load current IL (mA)	Load voltage VL (V)	Load power PL (mW)
1	500	8.00	4.00	32.00
2	750	6.86	5.14	35.27
3	1,000	6.00	6.00	36.00
4	1,500	4.80	7.20	34.56
5	2,200	3.75	8.25	30.94
6	3,300	2.79	9.21	25.70

Sample Calculation (RL = 1 kΩ):

IL = Vs/(Rs + RL) = 12/(1000 + 1000) = 0.006 A = 6 mA

VL = IL × RL = 0.006 × 1000 = 6 V

PL = VL²/RL = 6²/1000 = 0.036 W = 36 mW

Result:

Theoretical results show that the load receives maximum power when RL = Rth = 1 kΩ. At this point, VL = 6 V, IL = 6 mA, and PL = 36 mW. Verify this experimentally using measured readings.

Precautions:

Check all connections and polarity before switching ON the supply.
Use the correct meter range and connect the voltmeter in parallel with RL.
If measuring current directly, connect the ammeter in series; never connect an ammeter directly across the supply.
Switch OFF the supply before changing the load resistance.
Use resistors with suitable power ratings and avoid touching components that may become hot.
Do not record theoretical values as measured observations.

Viva-Voce Questions:

State the Maximum Power Transfer Theorem.
What is Thevenin resistance?
What is the condition for maximum power transfer in a DC resistive circuit?
What is the maximum load power for the circuit used in this experiment?
How does load power change when RL is much smaller or much larger than Rth?
State the maximum power transfer condition for AC circuits.
Does maximum power transfer also mean maximum efficiency? Explain briefly.

Note: For a purely resistive Thevenin source, maximum power transfer occurs at RL = Rth. At this condition, the ideal source resistance dissipates the same power as the load, so efficiency is 50%.