Question

Air isn't a perfect electric insulator, but it has a very high resistivity. Dry air has a resistivity of approximately 3×1013Ω×m. A capacitor has square plates 10 cm on a side separated by 1.2 mm of dry air. If the capacitor is charged to 250 V, what fraction of the charge will flow across the air gap in 1 minute? Make the approximation that the potential difference doesn't change as the charge flows.

Answer 1

Charge Between the plates of a capactior Q = CV

where C is Capaciatnce and V is Volatge

also C = KeoA/d

so charge Due to capacitance Q = 1 * 8.85 e -12 * 0.1 * 0.1* 250 /(1.2 e -3)

Q = 18.43 nC

Charge Q from ohms law is Q = it

also as V = iR

Current i = V/R

also Resistance R = rho L/.A

R = 3 e 13 * 1.2 e -3/(0.1* 0.1)

R = 3 6 e 12 ohms

i = 250/( 3.6 e 12)

i = 6.94 e -1Amps

Charge Q = it = 6.94 e-11 * 60 = 4.19 nC

fraction of charge Q /Qo = 4.19/18.43 = 0.227 or 22.7 %