Question

A parallel plate capacitor has a capacitance of \( 4 \, \mu\text{F} \). If the dielectric constant of the material between the plates is \( 5 \), what will be the new capacitance?

• A. \( 20 \, \mu\text{F} \)
• B. \( 15 \, \mu\text{F} \)
• C. \( 8 \, \mu\text{F} \)
• D. \( 10 \, \mu\text{F} \)

Hint:

Remember: The capacitance of a parallel plate capacitor increases by a factor of the dielectric constant when a dielectric is inserted between the plates.

Answer 1

The Correct Option is A

Step 1: Apply the formula for the capacitance of a parallel plate capacitor
The capacitance \( C \) of a parallel plate capacitor with a dielectric material is calculated using the formula:\[C = C_0 \times K\]where:- \( C_0 \) represents the capacitance without the dielectric (initial capacitance),- \( K \) is the dielectric constant.Step 2: Input the provided values
The given values are:- Initial capacitance \( C_0 = 4 \, \mu\text{F} \),- Dielectric constant \( K = 5 \).Substituting these values into the formula yields:\[C = 4 \, \mu\text{F} \times 5 = 20 \, \mu\text{F}\]Answer: The resultant capacitance is \( 20 \, \mu\text{F} \). Consequently, the correct option is (1).