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Question:

In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is:

14

12

34

1

Solution:

Heat generation in r will be, H = I²r, H = (V/(R+r) * r/(R+r))²r = (Vr/(R+r))²r = (VR/(R+2r))²r
Putting dH/dr = 0 gives, r = R/2. Hence, f = 1/2.