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A battery of e.m.f 10 V and internal resistance 0.5 Ω is connected across a variable resistance R. The value of R for which the power delivered in it is maximum is given by

Asked in CBSE AIPMT 1992 · Maximum power transfer

• (1) 0.5 Ω
• (2) 1.0 Ω
• (3) 2.0 Ω
• (4) 0.25 Ω

Step-by-step solution

Why the other options are wrong

• (2) Uses R=2r; the matching condition is R=r.
• (3) No single slip gives 2.0 Ω; at R=2 Ω the power is (100×2)/(2.5²)=32 W, below the 50 W reached at R=0.5 Ω.
• (4) Uses R=r/2; the matching condition is R=r.

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