A `600 cm` long potentiometer wire is connected to the circuit. The resistance of potentiometer wire is `15 r` (a) At what distance from the point A should the jockey touch the wire to gap zero deflection in the galvanometer ? (b) If the jockey touches the wire at a distance of `560 cm` from A, what will be the current in the galvanometer ?

Explanation

(a)
`p.d`. Across `AB, V_0 = (15 r)/(r + 15 r) xx E = (15)/(16) E`
No deflection in galvanometer i.e.,
`(((15 E)/(16)))/(600) =x = (E)/(2)`
`x = 320 cm`
(b) Resistance of `560 cm = (560)/(600) xx 15 r = 14 r`

`Lo op ①,path ABXYA`,
`V_A - i_2 xx 14 r -(i_1 + i_2) r - (i_1 + i_2) r + E = V_A`
`3 i_1 + 16 i_2 = E//r` ...(i)
`Lo op ②, path APZWA`,
`V_A - i_2 xx 14 r + i_1 r + (E )/(2) = V_A`
`-i_1 + 14 i_2 = E//2r` ..(ii)
Solving, `i_1 = (3E)/(22 r)`
Current in galvanometer `= 3E//22 r`.