Answer to Question #87336 in Electric Circuits for Udeh George

Question

Two identical cells each of e. m. f E and internal resistance r are first connected in series, and next in parallel. in each case they are applied across the two ends of a wire resistance R. it is found that the same current flows through the wire. what must be the relation between R and r?

Answer 1

In case of a serial connection of two identical e.m.f the current flowing in the circuit is

$$I_1 = \frac{2E}{2r + R}$$

In case of a parallel connection of two identical e.m.f. the current is

$$I_2 = \frac{E}{\frac{r}{2} + R}$$

Following the condition I₁ = I₂, we obtain

$$\frac{2E}{2r + R} = \frac{E}{\frac{r}{2} + R}$$

Solving this equation in respect to r, one can derive:

$$r = R$$

Answer: both r and R should be of the same value.