Electronics Labs, MAXIMUM POWER TRANSFER THEOREM Lab

This is Lab No.08 of Electrical & Electronics Engineering. This post explains about maximum power transfer theorem by practically on breadboard and theoretically by calculations. Read the lab manual carefully and if you have any further question, feel free to ask by commenting below.

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MAXIMUM POWER TRANSFER THEOREM Lab Manual:

Objective:

To Study and verify Maximum power transfer theorem

Apparatus:

  • Power supply
  • Digital Multimeter
  • Resistances
  • Bread Board
  • Jumper Wires

Procedure: 

In this experiment maximum power is transferred from the source to the Load when the resistance of the load is equal to the resistance of the source.

Proof for purely Resistive circuitsElectronics Labs, MAXIMUM POWER TRANSFER THEOREM Lab

In the diagram opposite, power is being transferred from the source, with voltage V and Fixed source resistance Rs, to a load with resistance RL, resulting in a current I, by ohm’s Law, I is simply the source voltage divided by the total circuit resistance:

            I = V / Rs + RL

The power PL Dissipated in the load is the square of the current multiplied by the Resistance:

            PL = I3 RL = (V/ Rs + RL) 2 RL = V2/ R2s/ RL + 2Rs + RL.

We could calculate the value of RL for witch this expression is a maximum, but it is Easier to calculate the value of RL for which the denominator

             R2s/ RL + 2Rs + RL

is a minimum. The result will be the same in either case. Differentiating with respect to RL:

d/dRL (R2s / RL + 2Rs + RL) = – R2s / R2L + 1.

For a maximum or minimum, the first derivation is zero, so

R2s / R2L =1

OR

RL = +Rs.

In practical, resistive circuits Rs and RL both positive. To find out whether this solution is a minimum or a maximum, we must differentiate again:  

          d2/dR2L(R2s/ RL + 2Rs + RL) = 2R2s/R3L

This is positive for positive values of Rs and RL, showing that the denominator is a Minimum, and power is therefore a maximum, when

              Rs =  RL.

Make up the circuit shown in the Figure.

Example-1Electronics Labs, MAXIMUM POWER TRANSFER THEOREM Lab

Rint>R L

RL = Rint + RL    

RT =  10 ohm + 5 ohm

RT = 15 ohm

IT = Vs/ RT = 20v / 15 ohm

= 1.33Amp

PL = I2  x  RL

=   (1.33 A)2  x  (5 ohm)

8.89 watts  

Example-2Electronics Labs, MAXIMUM POWER TRANSFER THEOREM Lab

RT = Rint  +  RL

RT = 10ohm + 10ohm

RT = 20ohm

IT =  Vs / RT = 20 v / 20

ohm =1Amp

PL = I2  x RL

(1A)2 x  (10 ohm)= 10 Watts

Example-3

RT = Rint + RLElectronics Labs, MAXIMUM POWER TRANSFER THEOREM Lab

RT = 10 ohm + 15 ohm

RT = 25 ohm

IT = Vs / RT = 20v / 25ohm

= 0.08Amp

PL = I2 x RL

= (0.80 A)2  x (15Ohm)

= 9.6 watts

Observations:

S/No A B C
1 Voltage 20 V
2 Rint 10 Kohm
3
4 RL IT PL
5
6
7
8
9
10
11
12

As we can clearly see, maximum power is transferred to the load when Rint is equal to the load resistance.

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