In the arrangement shows in fig. , when the switch `S_2` is open, the galvanometer shows no deflection for `l = L//2`. When the switch `S_2` is closed, the galvanometer shows no deflection for `l = 5//12L`. The internal resistance (r) of 6 V cell and the emf E of the other battery are, respectively

Options

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

Explanation

When switch `S_(1)` is open
`(6)/(E)=(L)/(2)//L=(1)/(2)`
`:. E=12 V`
When switch `S_(2)` is closed
`(6xx10)/(10+r)=(5)/(12)(L)/(L)xxE=(5)/(12)xx12=5`
`:. 10+r=12`
`:. r =2Omega`