The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant K. In the second case, it is filled with two slabs of equal thickness and dielectric constants K₁ and K₂ respectively as shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the relationship between K, K₁ and K_2.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$C_{1} = \frac{{kε}_{o} A}{d}$
Capacitor are connected in series
$\begin{array}{l} C_{2} = \frac{C^{'} C^{''}}{C^{'} + C^{''}} = (\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}) \frac{\in_{0} A}{d} \\ C_{1} = C_{2} \\ K = \frac{2 K_{1} K_{2}}{K_{1} + K_{2}} \end{array}$