In the arrangement shown in figure, when the switch S₂ is open, the galvanometer, shows no deflection for l=50 ~cm when the switch S₂ is closed, the galvanometer shows no deflection for l=0.416 ~m . The internal resistance (r) of 6 ~V cell is

Step-by-step solution

When S₂ open. Assume resistance of X Y=R . Resistance of wire per unit length, x= R L =R m ⁻¹ I=E₀ / R Now, the potential drop across 50 ~cm length is 6 ~V , So array cc & E₀ R R 50 100 =6 & E₀=12 ~V array When S₂ closed, potential drop across 0.416 ~cm length, V₁= E₀ R R 0.416=12 0.416 5 ~V Hence, E-I r=5 ~V aligned & & 6-I r & =5 & & I & = 5 10 & & 6-5 & = 5 10 r & & r & =2 aligned