# Potentiometer problem

Electricity and Magnetism Level 4

In the circuit of potentiometer, The length of the potentiometer wire $$AB$$ is $$50cm$$.The emf of the battery $$E_{1}$$ is $$4V$$, having negligible internal resistances.The values of resistances are $$R_{1}$$ and $$R_{2}$$ are $$15\Omega$$ and $$5\Omega$$ resp. When both the keys are open, the null point is obtained at a distance of $$31.25cm$$ from end A but when both the keys are $$closed$$, the balance length reduces to $$5cm$$ only.Given $$R_{AB}=10\Omega$$.The battery in secondary circuit has emf of $$E_{2}V$$ and internal resistance $$r\Omega$$.

Find the balance length (in cm) when key $$K_{2}$$ is open, and $$K_{1}$$ is closed.

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