A capacitor is filled with an insulator and a potential difference is applied to its plates. The energy stored in the capacitor is U. The capacitor is disconnected from the power source and the insulator is pulled out of it. The energy stored in the capacitor after the insulator is pulled out is 5U. What is the dielectric constant of the insulator?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
Once the capacitor is disconnected, the charge Q on the plates stays constant. Its energy is \( Q^{2}/2C \). The dielectric raises the capacitance from \( C_0 \) to \( KC_0 \). So removing the insulator multiplies the energy by \( K \).
\( \displaystyle U=\frac{Q^{2}}{2KC_0} \qquad\text{(with the insulator)} \)
\( \begin{aligned} U' &= \frac{Q^{2}}{2C_0} \\ &= KU \qquad\text{(insulator removed)} \end{aligned} \)
Putting \( U'=5U \):
\( KU=5U \)
\( \Rightarrow\; K=5 \)