In an electric circuit, the maximum power transferred to load resistance is 2Ω is 50 W. If now, the load resistance is changed to 8Ω, what will be the power transferred to the load?

Concept

The maximum power transfer theorem states that the maximum power is delivered to a load when the load resistance is equal to the source resistance.

The maximum power across the load is given by:

 \(P_{max}={V_{th}^2\over 4R_{th}}\) at condition \(R_L=R_{th}\)

Now, the power transferred to the load at other loading condition is given by:

\(P=I^2R_L\)

\(P=({V_{th}\over R_{th}+R_L})^2 \times R_L\)

Calculation

Given, P_max = 50 W at R_L = R_th =  2Ω 

\(50={V_{th}^2\over 4\times 2}\)

V_th = 20V

\(P=({20\over 2+8})^2 \times 8\)

P = 32 W