Question

When a capacitor of capacitance C is filled with a dielectric (i.e. thickness of the dielectric is equal to the spacing between the plates) of dielectric constant k, what is the new capacitance?

• A. $Ck$
• B. $\frac{C}{k}$
• C. $C{k}^2$
• D. $\frac{C}{k^2}$

Answer 1

The correct option is A $Ck$

When t=d for the dielectric introduced,
The formula for new capacitance,
$C^{\prime }=\frac{{\epsilon }_{0}A}{d-t+\frac{t}{k}}$
It changes to,
$C^{\prime }=\frac{k{\epsilon }_{0}A}{t}$
Since t=d,
C'=kC