Maximum Power Transfer Theorem

 

Experiment Name: Verification of Maximum Power Transfer Theorem

1. OBJECTIVE

To verify the Maximum Power Transfer Theorem in a DC network and to prove that maximum power is delivered to the load (R_L) when it is equal to the internal resistance (R_i) of the source.

 

2. APPARATUS REQUIRED

DC Power Supply: 0–30V
Fixed Resistor (R_i): 100 Ω
Decade Resistance Box (R_L): 0–500 Ω
Digital Multimeter: 2 units (to measure current and voltage)
Breadboard & Wires

 

3. CIRCUIT DIAGRAM

4. THEORY

The Maximum Power Transfer Theorem states that for a network to deliver maximum power to a load, the load resistance (R_L) must be equal to the internal resistance (R_i) of the source as seen from the load terminals.

Power delivered to the load:
P = I² × R_L
Where I = V / (R_i + R_L)
Maximum power occurs when dP/dR_L = 0, leading to R_i = R_L .

5. OBSERVATION TABLE

Constants: Source Voltage (V) = 10V, Internal Resistance (R_i) = 100 Ω

Reading No.	Load Resistance RL​ (Ω)	Current I (mA)	Load Voltage VL​ (V)	Power P (mW)
1	20	83.33	1.67	139.16
2	50	66.67	3.33	222.01
3	80	55.56	4.44	246.68
4	100	50.00	5.00	250.00
5	120	45.45	5.45	247.70
6	150	40.00	6.00	240.00
7	200	33.33	6.67	222.31

6. GRAPH

7. CALCULATION

At maximum power point:
Theoretical R_L = 100 Ω
P_max = V² / (4 × R_i)
P_max = 10² / (4 × 100) = 100 / 400 = 0.25 W = 250 mW

8. RESULT

It is observed that the maximum power is transferred to the load when R_L is equal to R_i. The experimental maximum power is 250 mW, which matches the theoretical calculation.

9. PRECAUTIONS

Tight Connections: Ensure all connections are tight to avoid extra resistance.
Component Heating: Avoid long operation as resistance may change.
Polarity Check: Ensure correct multimeter polarity.
Small Increments: Use small resistance steps near R_i.
Range Selection: Set proper multimeter range.
Zero Error Check: Ensure meters read zero before starting.