Question

Study the two circuits shown in the figure below. The cells in the two circuits are identical to each other. The resistance of the load resistor R is the same in both circuits.

If the same current flows through the resistor R in both circuits, calculate the internal resistance of each cell in terms of the resistance of resistor R. Show your calculations.

Answer 1

Current I in load resistance R is given by the formula,

I = `"E"/("R"+"r")`;

where E is the emf of the cell,

r is the internal resistance of the cell.

In circuit 1, the cells are in series.

∴ E_eq = 2E and r_eq = 2r

Current through R in circuit 1, I = `(2"E")/(("R"+2"r"))`

In circuit 2, the cells are in parallel.

∴ E_eq = E and r_eq = `"r"/2`

Current through R in circuit 2, I = `"E"/(("R"+"r"/2))`

Since the current is the same in both circuits,

`(2"E")/ (("R"+2"r")) = "E"/(("R"+"r"/2))`

Solving, we get r = R