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

Options

A. `3 Omega, 8 V`
B. `2 Omega, 12 V`
C. `2 Omega, 24 V`
D. `3 Omega, 12 V`

Answer

B

Explanation

(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`