Question

What is the working principle of maximum power transfer theorem?

Answer 1

The Maximum Power Transfer Theorem states that to transfer the maximum amount of power from a source to a load, the resistance of the load must be equal to the resistance of the source (or the Thevenin resistance if the source is represented by a Thevenin equivalent circuit).

Working Principle:

Here’s how it works:

1. Source and Load:
   

   Consider a simple circuit where there is a source (like a voltage source) and a load resistance connected in series with it.

1. Power Delivered to Load:
   

   The power delivered to the load resistance is given by the formula:
   
   \[
   P = \frac{V^2}{R_{\text{total}}}
   \]
   Where:
   - \(P\) is the power delivered to the load,
   - \(V\) is the voltage from the source,
   - \(R_{\text{total}}\) is the total resistance in the circuit, which is the sum of the source resistance and the load resistance.

1. Maximum Power Condition:
   

   To maximize the power delivered to the load, we need to adjust the load resistance.
   
   By using calculus and finding the point where the power with respect to load resistance \(R_L\) is maximized, it turns out that the power is maximum when the load resistance \(R_L\) is equal to the source resistance \(R_{\text{source}}\).

   \[
   R_L = R_{\text{source}}
   \]

1. Result:
   

   When the load resistance equals the source resistance, the power delivered to the load is at its maximum value. If the load resistance is higher or lower than the source resistance, the power delivered to the load decreases.

Key Points:

1. The theorem applies when the source resistance is purely resistive (no reactance).
   

1. The power is not necessarily maximized for maximum efficiency. In fact, efficiency is low under maximum power transfer, because half of the power is dissipated in the source resistance.
   

Example:

If you have a battery with a 10 Ω internal resistance and you connect a load to it, for maximum power transfer to the load, the load resistance should also be 10 Ω. This ensures that the power transferred to the load is maximized.