Question 49

When an external resistance of $$5\,\Omega$$ is connected across terminals of a cell, a current of $$0.25$$ A flow through it. When the $$5\,\Omega$$ resistor is replaced by a $$2\,\Omega$$ resistor, a current of $$0.5$$ A flow through it. The internal resistance of the cell is________ $$\Omega$$.

Correct Answer: 1

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

$$E = 0.25(5 + r) \quad \text{--- (Equation 1)}$$

$$E = 0.5(2 + r) \quad \text{--- (Equation 2)}$$

Since the cell remains the same, its $$\text{emf}$$ ($$E$$) is constant: $$0.25(5 + r) = 0.5(2 + r)$$

$$5 + r = 4 + 2r$$

$$r = 1\ \Omega$$

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