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A battery with EMF E and internal resistance r is connected across a resistance R. The power consumption in R will be maximum when

Asked in JEE Main 21st Jan 2nd Shift 2026 · Maximum power transfer

(1) R=r
(2) R=r/2
(3) R=2r
(4) R=√2r

Answer: (1) R=r

Step-by-step solution

P=(E²R)/((R+r)²).

Setting (dP)/(dR)=0 gives (R+r)²-2R(R+r)=0.

So R=r (maximum power transfer).

Why the other options are wrong

(2) Guess from halving r; at R=r/2 the power is only 8/9 of the maximum.
(3) Confuses with a doubling rule; at R=2r the power is again 8/9 of the maximum.
(4) No standard slip gives this; it would need P to depend on R² in the numerator.

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