Experiment 6: MPT Theorem

CTNA

Aim

To verify the Maximum Power Transfer Theorem.

Components and Equipment Required

  • Breadboard
  • Multimeter
  • Connecting wires
  • DC power supply
  • Resistor
  • Resistance box

Theory

According to the Maximum Power Transfer Theorem, a linear two-terminal network consisting of a voltage source and resistance will transfer maximum power to a load connected across its terminals when the load resistance $R_L$ is equal to the Thevenin’s resistance R_th of the network:

$R_L = R_{th}$

The power delivered to the load is maximum under this condition.

Formula Used

$P_{\text{max}} = \left( \frac{V_{\text{th}}}{R_1 + R_L} \right)^2 \cdot R_L $

Circuit Diagram

Circuit Diagram Circuit Diagram

Procedure

  1. Make the circuit on a breadboard with a resistance box as $R_L$.
  2. Connect a digital multimeter across $R_L$ to measure the load voltage $V_L$.
  3. Vary $R_L$ using the resistance box and note the corresponding $V_L$
  4. Calculate the power $P_L$ for each value of $R_L$.
  5. Plot $P_L$ as a function of $R_L$.

Observation Table

$R_L$ (Ω) $V_L$ (V) $P_L$ (W) $P_L$ (mW)

Result

The output power $P_L$ is maximum for $R_L = R_{th}$. Hence, the Maximum Power Transfer Theorem is verified.

Precautions

  • The output voltage of the power supply should remain constant during the experiment.
  • The internal resistance of the power supply, if any, is neglected.
  • The power supply should be switched off while making or breaking the circuit.