Question

A highly conducting sheet of aluminium foil of negligible thickness is placed between the plates of a parallel plate capacitor. The foil is parallel to the plates at distance $\frac{d}{2}$ from positive plate where $d$ is distance between plates. If the capacitance before the insertion of foil was $10\mu F$ , its value after the insertion of foil will be:

• A. $10\mu F$
• B. Zero
• C. $20\mu F$
• D. $5\mu F$

Answer 1

Answer: (A)

Initial capacitor $C=\frac{{ϵ}_{0}A}{d}=10\mu R$
After inserting aluminium foil the effective capacitor is series combination of $C_1=C_2=\frac{{ϵ}_{0}A}{\frac{d}{2}}$
$\therefore \frac{1}{C_{eff}}=\frac{1}{C_1}+\frac{1}{C_2}$
$\Rightarrow C_{eff}=\frac{C_1}{2}$
$\Rightarrow C_{eff}=\frac{{ϵ}_{0}A}{d}$
$\Rightarrow C_{eff}=10\mu F$