A capacitor is completely filled with a leaky dielectric. The capacitor is charged. It discharges with a time constant \(\tau = \rho k \epsilon_0\). The capacitor can be (Symbols have their usual meaning)
1. Parallel plate capacitor
2. Cylindrical capacitor
3. Spherical capacitor
4. Any of these
View Answer
For any capacitor geometry, capacitance is proportional to \(k\epsilon_0\) and resistance is proportional to resistivity \(\rho\), such that the shape factors cancel in \(\tau = RC = \rho k \epsilon_0\).
Assertion (A): Capacitor reduces sparks in induction coil.
Reason (R): Capacitor provides alternative path to current when circuit is broken.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
A: True. In an induction coil, breaking the circuit induces a high back EMF, causing sparks across the switch. Capacitors are used to mitigate this.
R: True. A capacitor connected across the switch provides a path for the induced current, absorbing the inductive energy and preventing excessive voltage buildup that leads to sparks.\n(R) correctly explains how (A) works.