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A cell of internal resistance r is connected to an extern...

A cell of internal resistance r is connected to an external resistor R. The conductor for maximum power transfer is?

A.

R < r

B.

R = r

C.

R = 2r

D.

R > r

Correct answer is B

Power = I2

= (ER+r)2R

To get point of maximum power transfer, we take the derivative and equate it to 0.

P=E2(R(R+r)2)

dPR=E2((R+r)22R(R+r)(R+r)4)

= E2((R+r)[(R+r)2R(R+r)4)

dPdR=E2(rR(R+r)3)

Maximum power is gotten when r - R = 0 i.e. r = R.