Question

A parallel plate capacitor filled with oil of a dielectric constant 3 between the plates has capacitance 'C'. If the oil is removed, then the capacitance of the capacitor will be

• A. $\frac{C}{3}$
• B. $3C$
• C. $\frac{3}{\sqrt{C}}$
• D. $\frac{\sqrt{C}}{3}$

Hint:

Adding a dielectric material always multiplies capacitance by a factor of $k$. Conversely, removing a dielectric material must divide the capacitance by that same factor of $k$. Since $k = 3$, the value drops straight to $\frac{C}{3}$!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A parallel plate capacitor initially contains a dielectric medium (oil with $k = 3$), yielding an overall capacitance value of $C$. We need to determine the new capacitance when the oil is drained, leaving only air or a vacuum between the plates.

Step 2: Key Formula or Approach:
The capacitance $C_d$ of a parallel plate capacitor containing a uniform dielectric material of constant $k$ is given by: $$ C_d = \frac{k \cdot \varepsilon_0 A}{d} $$ When the dielectric medium is removed and replaced by a vacuum or air, its dielectric constant drops down to $k_{\text{vacuum}} = 1$, giving the baseline capacitance: $$ C_0 = \frac{\varepsilon_0 A}{d} $$ This sets up the straightforward direct proportionality: $C_d = k \cdot C_0$.

Step 3: Detailed Explanation:
From the problem parameters:

• Initial capacitance with oil is $C_d = C$.

• The dielectric constant of the oil is $k = 3$.
Using our proportionality relationship: $$ C = 3 \cdot C_0 $$ To find the new capacitance after removing the oil ($C_0$), we isolate it by dividing by 3: $$ C_0 = \frac{C}{3} $$

Step 4: Final Answer:
The capacitance of the capacitor after removing the oil will be $\frac{C}{3}$, which corresponds to option (A).