SSC JE Electrical Engineering 2015 Paper

Question : 107 of 199

Marks: +1, -0

When a source is delivering maximum power to the load, the efficiency will be?

Solution:

The maximum power is transferred when the load resistance R

_L

is equal to internal Resistance R

_\th

or equivalent resistance R

_\th.

R_L=R _\th

I_L=V_ {\th}/{R _\th+R_L

P_L=I ^2_LR_ L

{dP_L}/{dR_L}=0=V_\th

then

R_{\th} = R_L

P_{\max}=V^2_{\th}/{4R_L}

Input power

P_{\in}=V_\th I=V_\th×V_\th/{2R_\th}=V^2_{\th}/{2R_\th}

efficiency =

P_L/P_{\in}={V^2_{\th}/{4R_\th}}/{V^2_{\th}/{2R_\th}}

=1/2=50%

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