Question

A parallel plate capacitor consists of two circular plates each of radius $12cm$ and separated by $5.0mm$. The capacitor is being charged by an external source. The charging current is constant and is equal to $0.15A$. The rate of change of potential difference between the plates will be :

• A. $8.173\times {10}^{7}V/s$
• B. $7.817\times {10}^{8}V/s$
• C. $1.873\times {10}^{9}V/s$
• D. $3.781\times {10}^{10}V/s$

Answer 1

The correct option is C $1.873\times {10}^{9}V/s$

Cross section area of plate , $A=\pi r^2=\pi \times (0.12{)}^2{m}^2$

Separation $d=5mm=5\times {10}^{-3}m$

Potential difference plates is $V=Ed=\frac{q}{A{ϵ}_0}d=\frac{itd}{A{ϵ}_0}$ where $i=q/t$ and $t=$time

so the rate of change of potential difference between the plates $=V/t=\frac{id}{A{ϵ}_0}=\frac{0.15\times 5\times {10}^{-3}}{\pi \times (0.12{)}^2\times 8.85\times {10}^{-12}}=1.873\times {10}^{9}V/s$