Question

A parallel plate capacitor has capacitance $C$. If a dielectric slab of dielectric constant $K$ and thickness equal to half the plate separation is introduced parallel to the plates, the new capacitance is:

• A. $\dfrac{2K}{K+1}\,C$
• B. $\dfrac{K+1}{2K}\,C$
• C. $\dfrac{K}{K+1}\,C$
• D. $KC$

Hint:

Think of the system as two capacitors in series: $C_{air} = \dfrac{\varepsilon_0 A}{d/2}$ and $C_{dielectric} = \dfrac{K\varepsilon_0 A}{d/2}$. Their series combination gives $\dfrac{2K}{K+1}C$.

Answer 1

The Correct Option is A