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 (Ri): 100 Ω
Decade Resistance Box (RL): 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 × RL
Where I = V / (Ri + RL)
Maximum power occurs when dP/dRL = 0, leading to Ri = RL
.
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.