A capacitor stores a charge of \( 10\,\mu\mathrm{C} \) when connected across a battery. When the gap between the plates is filled with a dielectric, a further charge of \( 20\,\mu\mathrm{C} \) flows through the battery. Find the dielectric constant of the dielectric.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → K = 3
The capacitor stays connected to the battery, so the potential difference V stays the same. Filling the gap with a dielectric raises the capacitance from \( C \) to \( KC \). So the charge rises from \( Q_0=CV \) to \( Q=KCV \), and \( K=Q/Q_0 \).
The charge with the dielectric is:
\( \begin{aligned} Q &= Q_0+\Delta Q \\ &= 10\,\mu\mathrm{C}+20\,\mu\mathrm{C} \\ &= 30\,\mu\mathrm{C} \end{aligned} \)
\( \begin{aligned} K &= \frac{Q}{Q_0} \\ &= \frac{30\,\mu\mathrm{C}}{10\,\mu\mathrm{C}} \\ &= 3 \end{aligned} \)