The internal resistance $r$ of a cell determined using a potentiometer is given by the formula $r = R \left( \frac{l_1}{l_2} - 1 \right)$, where $l_1$ is the balancing length in open circuit, $l_2$ is the balancing length when external resistance $R$ is connected, and $R$ is the external resistance.

Given: $l_1 = 76.3 \text{ cm}$ $l_2 = 64.8 \text{ cm}$ $R = 9.5 \ \Omega$

Substituting these values: $r = 9.5 \times \left( \frac{76.3}{64.8} - 1 \right)$ $r = 9.5 \times (1.1775 - 1)$ $r = 9.5 \times 0.1775 \approx 1.686 \ \Omega$.

Rounding to two decimal places gives 1.69 \Omega , but 1.68 \Omega is the closest valid option provided.