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Question

# A battery of internal resistance, 3Ω is connected to 20Ω resistor and potential difference across the resistor is 10 V. If another resistor of 30Ω is connected in series with the first resistor and battery is again connected to the combination calculate the e.m.f. and terminal potential difference across the combination.

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Solution

## Let the emf of the battery be E.Internal resistance of battery r=3Ω.Voltage across the resistor 20Ω is 10 volts.Voltage across resistor 20Ω V=RR+rE∴ 10=2020+3E⟹ E=11.5 voltsNow another resistor 30Ω is connected in series with battery and previous resistor.Total resistance of the circuit Req=30+20+3=53ΩCurrent flowing through the circuit I=EReq∴ I=11.553=0.22 AThus terminal potential difference across the combination V′=I(20+30)∴ V′=0.22×50=11 volts

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