In the arrangement shown in figure when the switch `S_2` is open, the galvanometer shown no deflection for `l=L//2`. When the switch `S_2` is closed, the galvanometer shown no deflection for `l=5L//12`. The internal resistance `(r)` of `6V` cell, and the emf `E` of the other battery are respectively A. `3 Omega, 8 V`B. `2 Omega, 12 V`C. `2 Omega, 24 V`D. `3 Omega, 12 V`

In the arrangement shown in figure when the switch `S_2` is open, the

1.	In the arrangement shown in figure when the switch `S_2` is open, the galvanometer shown no deflection for `l=L//2`. When the switch `S_2` is closed, the galvanometer shown no deflection for `l=5L//12`. The internal resistance `(r)` of `6V` cell, and the emf `E` of the other battery are respectively A. `3 Omega, 8 V`B. `2 Omega, 12 V`C. `2 Omega, 24 V`D. `3 Omega, 12 V`
Answer» Correct Answer - B (b) When `S_(2)` open Assume resistance of `AB = R` Resistance of wire per unit length. `x = (R )/(L)` `I = (E)/(R )` Now in `AC` `(E)/(R ) xx (R )/(L) xx (L)/(2) = 6` `E = 12 V` When `S_(2)` closed `V_(1) = (E)/(R ) xx (R )/(L) xx (5L)/(12) = (5R)/(12) = (5 xx 12)/(12) = 5V` `implies 6 - I_(1) r = 5 implies 6 - ((5)/(10)) r = 5 implies r = 2 Omega`

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