EXPERIMENT NO.: 04
NAME OF EXPERIMENT: Study and Verify the Maximum Power Transfer Theorem
OBJECTIVE:
The primary objective of this experiment is to study and verify the Maximum Power Transfer
Theorem by examining the relationship between the load resistance (RL) and the power
delivered to it in a simple resistive circuit. The experiment aims to confirm that maximum
power is transferred when the load resistance is equal to the source resistance.
THEORY:
The Maximum Power Transfer Theorem states that the maximum power is transferred from
the source to the load when the load resistance (RL) is equal to the Thevenin resistance (RTH)
as seen from the load.
Given a circuit with a voltage source VTH and the Thevenin
resistance RTH in series with the load resistor RL , the power
delivered to the load is given by:
𝑃=(
2
𝑉𝑇𝐻
) × 𝑅𝐿
𝑅𝑇𝐻 + 𝑅𝐿
To find the value of RL that maximizes the power delivered to the load, we differentiate the
above expression with respect to RL and set it equal to zero. The resulting condition for
maximum power transfer is:
𝑅𝐿 = 𝑅𝑇𝐻
The maximum power transferred to the load is then:
𝑉𝑇𝐻 2
𝑃𝑚𝑎𝑥 =
4 𝑅𝑇𝐻
This relationship forms the basis for the experiment and serves as the theoretical prediction
that will be verified.
LIST OF COMPONENTS:
•
Ammeter (1 pieces; 0-5A)
•
Voltmeter (1 pieces; 0-450V)
•
Wattmeter (1 piece; 0-2A, 0-120V)
•
Resistor (2 pieces; 106.7 Ω, 370Ω)
•
AC voltage source (220V)
•
Connecting wires
CIRCUIT DIAGRAM:
Fig.: Verifying Maximum Power Transfer Theorem
DATA TABLE:
Supplied Thevenin’s
Load
SL Voltage, Resistance, Resistance,
No.
Vs
Rth
RL
(V)
(Ω)
(Ω)
Voltage Current
𝑬𝒓𝒓𝒐𝒓
across through Measured Calculated
𝑷𝒄 − 𝑷
load,
load,
Power, P
Power, Pc =
𝑷𝒄
𝑽𝑹𝑳
𝑰𝑹𝑳
(W)
(W)
× 𝟏𝟎𝟎%
(V)
(A)
01
02
03
04
05
73.10
65.70
52.30
50.00
44.16
100.9
290.6
205.0
120.1
106.3
90.13
106.7
0.22
0.30
0.42
0.44
0.49
14
15
17
18
17
16.08
19.71
21.97
22.00
21.64
GRAPH OF DATA:
20
17
18
18
17
15
16
14
Power (W)
14
12
10
8
6
4
2
0
0
50
100
150
200
Resistance (Ω)
CALCULATION AND RESULTS:
For observation -01:
Measured Power, P = 14
Actual Power Calculated, Pcal = 16.08
250
300
350
12.93
23.83
22.62
18.18
21.44
𝐸𝑟𝑟𝑜𝑟 =
𝑃𝑐 − 𝑃
𝑃𝑐
× 100% = 12.93%
For observation -02:
Measured Power, P = 15
Actual Power Calculated, Pcal = 19.71
𝐸𝑟𝑟𝑜𝑟 =
𝑃𝑐 − 𝑃
𝑃𝑐
× 100% = 23.83%
For observation -03:
Measured Power, P = 17
Actual Power Calculated, Pcal = 21.70
𝐸𝑟𝑟𝑜𝑟 =
𝑃𝑐 − 𝑃
𝑃𝑐
× 100% = 21.97%
For observation -04:
Measured Power, P = 18
Actual Power Calculated, Pcal = 22.00
𝐸𝑟𝑟𝑜𝑟 =
𝑃𝑐 − 𝑃
𝑃𝑐
× 100% = 18.18%
For observation -05:
Measured Power, P = 17
Actual Power Calculated, Pcal = 21.64
𝐸𝑟𝑟𝑜𝑟 =
𝑃𝑐 − 𝑃
𝑃𝑐
× 100% = 21.44%
CONCLUSION AND DISCUSSION:
The results of the experiment confirm the validity of the Maximum Power Transfer Theorem.
The maximum power was indeed transferred when the load resistance was equal to the
source resistance. The experimental findings closely matched the theoretical predictions,
demonstrating that the Maximum Power Transfer Theorem is a reliable principle for
optimizing power transfer in resistive circuits. Measurement inaccuracies due to limitations
of the multimeter or ammeter, Tolerance of resistors, which might cause slight deviations in
the expected resistance values and Measurement inaccuracies due to limitations of the
multimeter or ammeter.