Question

In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3}{m}^2$ and the distance between the plates is $3mm$. Calculate the capacitance of the capacitor. If this capacitor is connected to a $100V$ supply, what is the charge on each plate of the capacitor?

Answer 1

Step 1: Find the capacitance of the capacitor.

Area of each plate, $A=6\times {10}^{-3}{m}^2$

Distance between the plates,$d=3mm=0.003m$

Capacitance of capacitor,

$C=\frac{A{ϵ}_0}{d}$

$\therefore C=\frac{6\times {10}^{-3}\times 8.85\times {10}^{-12}}{0.003}=17.7pF$

Step 2: Find the charge on each plate of the capacitor.

Voltage across the capacitor, $V=100V$

Thus, charge on each plate, $Q=CV$

$\therefore Q=17.7\times {10}^{-12}\times 100$

$\Rightarrow Q=1.77\times {10}^{-9}C$