1 Answer
The efficiency of maximum power transfer refers to how effectively the power from a source is transferred to the load in a circuit. According to the Maximum Power Transfer Theorem, maximum power is transferred to the load when the load resistance (\(R_L\)) is equal to the source resistance (\(R_s\)).
Formula for Efficiency:
The efficiency (\(\eta\)) of maximum power transfer is given by:
\[
\eta = \frac{P_{out}}{P_{in}} \times 100
\]
Where:
When the load resistance equals the source resistance (i.e., \(R_L = R_s\)), the efficiency is at its maximum. However, this is generally not very high because half of the power is dissipated in the source resistance.
Efficiency at Maximum Power Transfer:
The maximum efficiency can be calculated as:
\[
\eta_{max} = \frac{P_{out}}{P_{in}} = \frac{R_L}{R_s + R_L}
\]
When \(R_L = R_s\), this simplifies to:
\[
\eta_{max} = \frac{R_s}{2R_s} = 0.5 \quad \text{or} \quad 50\%
\]
So, the maximum efficiency of power transfer in a resistive circuit is 50% when the load resistance equals the source resistance.
Key Points:
This efficiency is not ideal for many practical applications, as the goal is often to maximize the power delivered to the load rather than achieving maximum power transfer.
Formula for Efficiency:
The efficiency (\(\eta\)) of maximum power transfer is given by:\[
\eta = \frac{P_{out}}{P_{in}} \times 100
\]
Where:
- \(P_{out}\) is the power delivered to the load.
- \(P_{in}\) is the total power supplied by the source.
When the load resistance equals the source resistance (i.e., \(R_L = R_s\)), the efficiency is at its maximum. However, this is generally not very high because half of the power is dissipated in the source resistance.
Efficiency at Maximum Power Transfer:
The maximum efficiency can be calculated as:\[
\eta_{max} = \frac{P_{out}}{P_{in}} = \frac{R_L}{R_s + R_L}
\]
When \(R_L = R_s\), this simplifies to:
\[
\eta_{max} = \frac{R_s}{2R_s} = 0.5 \quad \text{or} \quad 50\%
\]
So, the maximum efficiency of power transfer in a resistive circuit is 50% when the load resistance equals the source resistance.
Key Points:
- Maximum power transfer occurs when the load resistance is equal to the source resistance.
- The efficiency of maximum power transfer is 50% because half of the power is dissipated in the source resistance and the other half is delivered to the load.
This efficiency is not ideal for many practical applications, as the goal is often to maximize the power delivered to the load rather than achieving maximum power transfer.