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: Recall how a dielectric changes capacitance.
With a dielectric of constant $k$, the capacitance is $k$ times its empty (air) value. So $C=k\,C_0$.

Step 2: Put in the numbers.
Here $k=3$ and the filled value is $C$, so $C=3\,C_0$.

Step 3: Solve for the empty capacitance.
\[ C_0=\frac{C}{3} \]
\[ \boxed{\frac{C}{3}} \]