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Question

# A battery having emf 10 V and internal resistance 2 Ω is connected to an external circuit as shown in the diagram. Find the value of R for which maximum power will be transferred to the external circuit. Also find the efficiency of the battery.

A
3 Ω,50%
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B
4 Ω,50%
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C
2 Ω,67%
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D
4 Ω,67%
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Solution

## The correct option is A 3 Ω,50%We know that for maximum power trasfer, external resistance should be equal to internal resistance of the battery. Consider the external circuit, we can observe that 3 Ω and R are connected in series. These resistances are in parallel combination. Their equivalent resistance, Req=3×(3+R)3+(3+R). From maximum power transfer theorem, Req=2 ⇒3×(3+R)3+(3+R)=2 ⇒9+3R=12+2R ∴R=3 Ω Current in the circuit, i=102+2=2.5 A Now, Efficiency =PoutPin×100 Input power, Pin=E×i=10×2.5=25 W Output power, Pout=i2Req=2.52×2=12.5 W Therefore, efficiency =50%

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