Question

A parallel plate capacitor having a plate area of 0.70 m2 and a plate separation of 1.0 mm is connected to a source with a voltage of 50 V. Find the capacitance, the charge on the plates, and the energy of the capacitor a) when there is air between the plates

Answer 1

The capacitance of the air-filled capacitor can be found as follows:

$$C=\dfrac{\epsilon_0A}{d},$$ $$C=\dfrac{8.85\cdot10^{-12}\ \dfrac{F}{m}\cdot0.7\ m^2}{1.0\cdot10^{-3}\ m}=6.2\cdot10^{-9}\ F=6.2\ nF.$$

The charge on the plates can be found as follows:

$$Q=CV=6.2\cdot10^{-9}\ F\cdot50\ V=3.1\cdot10^{-7}\ C.$$

The energy stored in the capacitor can be found as follows:

$$E=\dfrac{1}{2}CV^2,$$ $$E=\dfrac{1}{2}\cdot6.2\cdot10^{-9}\ F\cdot(50\ V)^2=7.75\cdot10^{-6}\ J.$$