Question

Four capacitors of equal capacity are connected in series with a battery of 20 V. The middle point O is earthed. Calculate the potential at points P and Q. \includegraphics[width=0.5\linewidth]{image3.png}

Hint:

For capacitors in series, the voltage is divided equally if the capacitors are identical. The total charge on all capacitors is the same.

Answer 1

Let the capacitance of each capacitor be \( C \) and the total voltage of the battery is \( V = 20~\text{V} \). Since the capacitors are connected in series, the equivalent capacitance of the series combination is given by: \[ \frac{1}{C_{\text{eq}}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{4}{C} \] Thus, the equivalent capacitance is: \[ C_{\text{eq}} = \frac{C}{4} \] Now, using the relation for voltage and charge in a capacitor, the potential difference across each capacitor is: \[ V_{\text{cap}} = \frac{V}{4} = \frac{20}{4} = 5~\text{V} \] Therefore, the potential at point \( P \) is 20 V (since it is connected directly to the battery) and the potential at point \( Q \) is 0 V (since it is earthed). Thus, the potential at \( P \) is 20 V and at \( Q \) is 0 V.