Verification of Maximum Power Transfer Theorem

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Aim

Verification of Maximum Power Transfer Theorem

Apparatus

Breadboard, Batteries or DC regulated power supply, Resistors, Digital multimeter, Connecting wires, Alligator clips, Computer and Multisim software for simulation.

Theory

Statement

The maximum power transfer theorem states that in a linear, bilateral DC network, maximum power is delivered to the load when the load resistance is equal to the internal resistance of a source.

verification of Maximum power transfer theorem
Figure 1: Concept of maximum power transfer theorem

RS = Source resistance also called Thevenin’s resistance

RL = Load resistance

V = Source applied

I = Current flowing through the circuit

Steps to calculate Pmax by using Maximum power transfer theorem

Verification of Maximum power transfer theorem
Figure 2: Block diagram of two terminal linear network
  1. Remove the variable load resistor RL.
  2. Find the open circuit voltage VTH across points A and
  3. Find the resistance RTH as seen from points A and
  4. Find the resistance RLfor maximum power
  5. Find the current

    {I_L} = \frac{{{V_{TH}}}}{{{R_{TH}} + {R_L}}} = \frac{{{V_{TH}}}}{{2{R_{TH}}}}

  6. Find the maximum power by using formula

    {P_{\max }} = I_L^2{R_L}

\therefore {P_{\max }} = \frac{{V_{TH}^2}}{{4R_{TH}^2}}{R_{TH}} = \frac{{V_{TH}^2}}{{4{R_{TH}}}}

 

OR

{P_{\max }} = \frac{{V_{TH}^2}}{{4{R_L}}}

Applications of maximum power transfer theorem

  • In radio communication, there is often a requirement to match the source impedance (at the transmitter) to the load impedance (such as an antenna) to avoid reflections in the transmission line that could overload or damage the transmitter.
  • It is also applied in audio systems, where the voice is to be transmitted to the speaker. The amplifier amplifies the maximum amount of voice when the load impedance is equal to the source impedance.
  • In car or any automobiles, if the effective resistance of the motor and the internal resistance of the battery are equal  then  maximum power will be transferred from battery to the motor to turn ON the engine.

Circuit Diagram

experimental set up of verification of maximum power transfer theorem,
Figure 3: Circuit diagram for experimental set-up of maximum power transfer theorem

[You can take any value of source resistance RTH and then can vary load resistor with respect to RTH , accordingly make changes in observation table.]

Procedure

  1. Connect the circuit as shown in the figure 3.
  2. Vary the load resistor RL in steps of 100Ω and take the readings of voltmeter (VL) and ammeter (IL) for different values of RL.
  3. Take 10 to 15 readings as per observation table.
  4. Calculate power P for each value of RL.
  5. Plot the graph RL on X-axis versus power P on Y-axis.

Precautions

  • Before circuit connection working condition of all the components must be checked.
  • All the connection should be tight.
  • Ammeter must be connected in series while voltmeter must be connected in parallel to the components (resistors).
  • The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.

Observation table

Sr. No.

RL (Ω)

VL (V)

IL (mA)

P= VL IL (mW)

1.      

500Ω

 

 

 

2.      

600Ω

 

 

 

3.      

700Ω

 

 

 

4.      

800Ω

 

 

 

5.      

900Ω

 

 

 

6.      

1000Ω

 

 

 

7.      

1100Ω

 

 

 

8.      

1200Ω

 

 

 

9.      

1300Ω

 

 

 

10.  

1400Ω

 

 

 

11.  

1500Ω

 

 

 

12.  

1600Ω

 

 

 

Calculations

RS = RTH = 1KΩ

V = VTH = 10V

Theoretically maximum power delivered by the source to load resistance,

Result

Calculated maximum power delivered by the source to load resistance Pmax=

Practically maximum power delivered by the source to load resistance Pmax=

Conclusion

Power delivered by the source to load resistor is maximum when load resistance is equal to source resistance (RL = RS). Also Theoretical and practical value of maximum power is found to be nearly same hence maximum power transfer theorem is verified.

Video Tutorial on Maximum Power Transfer Theorem

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