In the arrangement shown in figure, when the switch S_2 is open, the galvanometer, shows no deflection for l=50 ~cm when the switch S_2 is closed, the galvanometer shows no deflection for l=0.416 ~m . The internal resistance (r) of 6 ~V cell is
A. 2
When S_2 open. Assume resistance of X Y=R. Resistance of wire per unit length, x= R L =R m ^ -1 I=E_0 / R Now, the potential drop across 50 ~cm length is 6 ~V , So array cc & E_0 R R 50 100 =6 \\ & E_0=12 ~V array When S_2 closed, potential drop across 0.416 ~cm length, V_1= E_0 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
Related: Physics — Current Electricity · All PYQ Banks