A battery of emf `E_(0) = 12 V` is connected across a `4 m` long uniform wire having resistance `(4 Omega)/(m)`. The cells of small
emfs `epsilon_(1) = 2 V` and `epsilon_(2) - 4 V` having internal resistance `2 Omega` and `6 Omega` respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point `N`, the distance of point `N` from teh point `A` is equal to

Options

A. `(1)/(6) m`
B. `(1)/(3) m`
C. `25 cm`
D. `50 cm`

Answer

C

Explanation

(c ) Potential gradient
`x = ((12)/(8 + 16)) xx 4 = 2 Vm^(-1)`
Effective emf of `E_(1)` and `E_(2)`
`ul(E_(2)) - ul(E_(2))`
`E = (r_(2) r_(1))/(1 // r_(1) + 1 // r_(2)) = (1)/(2)` volt
Balancing length `= ((1)/(2))((1)/(2)) = (1)/(4) = m = 25 cm`