Question

If 'r' is the internal resistance of a cell, such that 'E' is its e.m.f. and 'V' the p.d. and R the external resistance of the circuit, then the expression for internal resistance is:

Options

• $$r = \frac{\mathrm{R}(\mathrm{E} - \mathrm{V})}{\mathrm{V}}$$

• $$r = \frac{\mathrm{E} - \mathrm{V}}{\mathrm{RV}}$$

• $$r = \frac{\mathrm{V}}{\mathrm{R}(\mathrm{E} - \mathrm{V})}$$

• none of these

Answer 1

$$r = \frac{\mathrm{R}(\mathrm{E} - \mathrm{V})}{\mathrm{V}}$$

Explanation:

From Ohm's law, $$I = \frac{V}{R}$$

Whole circuit, $$I = \frac{E}{R+r}$$

Equating: $$\frac{V}{R} = \frac{E}{R+r}$$

$$VR + Vr = ER$$

$$Vr = R(E - V)$$ and $$r = \frac{R(E - V)}{V}$$