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Potentiometer wire PQ of 1 m length is c...

Potentiometer wire `PQ` of `1 m` length is connected to a standard cell `E_(1)`. Another cell `E_(2)` of emf `1.02 V` is connected with a resistance `r` and a switch `S` as shown in the circuit diagram. With switch `S` open, the null position is obtained at a distance of `51 cm` from `P`.
(i) Calculate the potential gradient of the potentiometer wire.
(ii) Find the emf of cell `E_(1)`.
(iii) When switch `S` is closed, will the null point move toward `P` or toward `Q`? Give reason for your answer.

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