Question

Two cells of the same emf E but different internal resistances r₁ and r₂ are connected to an external resistance R as shown in the figure given below. The voltmeter V reads zero. Obtain an expression for R in terms of r₁ and r₂. (Assume that the voltmeter V is of infinite resistance).

Answer 1

The total emf in the circuit is,

E + E = 2E

The total resistance in the circuit is,

R + r₁ + r₂

The current in the circuit is given by:

I = `(2 E)/(R +r_1 + r_2)`

Given, V = E − I r₁ = 0

∴ I r₁ = E

∴ `(2 E)/(R + r_1 + r_2) xx r_1` = E

R = r₁ − r₂