Question

The parallel plate capacitor on the left $CL$ has a separation distance of $1cm$, and the sides of the square plate are each $0.5m$. While the smaller parallel plate capacitor on the right $CR$ has a separation distance of $0.2cm$ and each side of the square plate is $0.1m$ in length.
Determine the ratio of capacitance $CL:CR$.

• A. 1:1
• B. 5:1
• C. 1:5
• D. 3:1

Answer 1

Answer: (B)

5:1

Capacitance of parallel plate capacitor $C=\frac{A{ϵ}_o}{d}$

For $CL$ : $d=1cm=0.01m$ $A=(0.5{)}^2$ $m^2$

$\therefore$ $CL=\frac{(0.5{)}^2{ϵ}_o}{0.01}=25{ϵ}_o$

For $CR$ : $d=0.2cm=0.002m$ $A=(0.1{)}^2$ $m^2$

$\therefore$ $CL=\frac{(0.1{)}^2{ϵ}_o}{0.002}=5{ϵ}_o$

$⟹$ $CL:CR=5:1$