A parallel plate capacitor with air between the plates has each plate with an area of \(6 \times 10^{-3}~\text m^2\) and a separation of \(3~\text{mm}.\) If this capacitor is connected to a \(100~\text{V}\) supply, what is the capacitance of the capacitor and the magnitude of the charge on each plate, respectively?
1. \(1.77 \times 10^{-11}~\text F~\text{and}~1.77\times~10^{-9}~\text C\)
2. \(1.77 \times 10^{-12}~\text F~\text{and}~1.77\times~10^{-10}~\text C\)
3. \(1.77 \times 10^{-13}~\text F~\text{and}~1.77\times~10^{-11}~\text C\)
4. \(1.77 \times 10^{-14}~\text F~\text{and}~1.77\times~10^{-12}~\text C\)
Given,
The area of plate of the capacitor, A = 6 x 10-3 m2
Distances between the plates, d = 3mm = 3 x 10-3 m
Voltage supplied, V = 100v
Capacitance of a parallel plate capacitor is given by,
Here,
ε = permittivity of free space = 8.854 × 10-12 N-1 m -2 C-2
Therefore, each plate of the capacitor is having a charge of
q = VC = 100 × 17.81 x 10-12 C = 1.771 x 10-9 C
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