A cell of internal resistance r is connected to an external resistor R. The conductor for maximum power transfer is?
-
A.
R -
B.
R = r -
C.
R = 2r -
D.
R > r
Correct Answer: Option B
Explanation
Power = I(^2)R
= ((frac{E}{R + r})^2 R)
To get point of maximum power transfer, we take the derivative and equate it to 0.
(P = E^2 (frac{R}{(R + r)^2}))
(frac{mathrm d P}{mathrm R} = E^2 (frac{(R + r)^2 – 2R(R + r)}{(R + r)^4}))
= (E^2 (frac{(R + r)[(R + r) – 2R}{(R + r)^4}))
(frac{mathrm d P}{mathrm d R} = E^2 (frac{r – R}{(R + r)^3}))
Maximum power is gotten when r – R = 0 i.e. r = R.