2nd Reminder: Please answer: A potentiometer circuit consists of a resistance r in the primary and secondary circuit both - Physics - Electromagnetic Induction

Question

2nd Reminder: Please answer:
A potentiometer circuit consists of a resistance r in the
primary and secondary circuit both the potentiometer wire is 600 cm
long and its resistance is 15r emf of driving cell is E and the emf
of the experimental cell is E/2 1 at what distance from the leftend
should the jockey touch the wire to get zero deflection int the
galvanometer 2 if the jockey touches the wire at a distance 560 cm
from the left end , what will be the current in the galvanometer
?

Himanshu · Accepted Answer

1 Let the jockey divide the 600 cm length into two parts as shown below:

$\frac{E}{2} = (15 âˆ’ x) r I_{1} â‡’ E = 2 (15 âˆ’ x) r I_{1} E = (15 âˆ’ x) r I_{1} + (1 + x) r (I_{1}) = 16 r I_{1} 2 (15 âˆ’ x) = 16 â‡’ 2 x = 14 â‡’ x = 7$ Let the jockey be placed at a distance of y cm from the left Therefore, $\frac{y}{600 âˆ’ y} = \frac{15 âˆ’ x}{x} = \frac{8}{7} â‡’ 7 y = 4800 âˆ’ 8 y â‡’ y = \frac{4800}{15} = 320 â¢ â€‰ â€‰ â€‰ c m$ 2 Since, 600 cm = 15r, therefore, 560 cm will be equal to 14r The diagram of the equivalent circuit is given below

$\frac{E}{2} = 14 r (I_{1} + I_{2}) + I_{2} r â‡’ E = r (28 I_{1} + 30 I_{2}) E = 14 r (I_{1} + I_{2}) + 2 r (I_{1}) = r (16 I_{1} + 14 I_{2}) S o l v i n g â¢ â€‰ â€‰ â€‰ t h e â¢ â€‰ â€‰ â€‰ a b o v e â¢ â€‰ â€‰ e q u a t i o n s â¢ â€‰ â€‰ â€‰ w e â¢ â€‰ â€‰ g e t â¢ â€‰ â€‰ I_{2} = \frac{3 E}{22 r}$