A cell having an emf $$\varepsilon $$ and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by

The power dissipated in the circuit shown in the figure is 30 watts. The value of R is

In the circuit shown the cells A and B have negligible resistances. For V_A = 12 V, R₁ = 500 $$\Omega $$ and R = 100 $$\Omega $$ the galvanometer (G) shows no deflection. The value of V_s is

A ring is made of a wire having a resistance R₀ = 12 $$\Omega $$. Find the points A and B, as shown in the figure, at which a current carrying conductor should be connected so that the resistance R of the sub circuit between these point is equal to $${8 \over 3}\Omega $$.