Question

The area of the plates of a parallel plate condenser is A and the distance between the plates is 10 mm. There are two dielectric sheets in it, one of dielectric constant 10 and thickness 6 mm and the other of dielectric constant 5 and thickness 4 mm, the capacity of the condenser is:-

• A. $\frac{12}{35}$ ${ϵ}_{0}A\times {10}^{-3}$
• B. $\frac{2}{3}$ ${ϵ}_{0}A\times {10}^{-3}$
• C. $\frac{5}{7}$ ${ϵ}_{0}A\times {10}^{-3}$
• D. $\frac{21}{13}$ ${ϵ}_{0}A\times {10}^{-3}$

Answer 1

The correct option is C $\frac{5}{7}$ ${ϵ}_{0}A\times {10}^{-3}$

Apply this formula $C_{eq}=\frac{{ϵ}_{0}A}{d-t_1(1-\frac{1}{k_1})-t_2(1-\frac{1}{k_2})}$

where $t_1=6,t_2=4,k_1=10,k_2=5,d=10mm$

$C_{eq}=\frac{{ϵ}_{0}A}{10-6(1-\frac{1}{10})-4(1-\frac{1}{5})}=\frac{5}{7}\times {10}^{-3}{ϵ}_{0}A$