Question

The capacitance of a parallel plate capacitor with air as dielectric is \( C \). If a slab of dielectric constant \( K \) and of the same thickness as the separation between the plates is introduced so as to fill \( \frac{1}{4} \)th of the capacitor (shown in figure), then the new capacitance is

• A. \( (K+1) \frac{C}{4} \)
• B. \( (K+3) \frac{C}{4} \)
• C. \( (K+1) \frac{C}{2} \)
• D. None of these

Hint:

When a dielectric is inserted into a capacitor, it increases the capacitance by a factor related to the dielectric constant \( K \).

Answer 1

The Correct Option is B

Step 1: Capacitance with dielectric.
When a dielectric slab is introduced into a capacitor, the capacitance increases by a factor depending on the dielectric constant. The new capacitance is calculated based on the volume fraction of the dielectric inserted into the capacitor.

Step 2: Conclusion.
The new capacitance is \( (K+3) \frac{C}{4} \), which corresponds to option (2).