A large air-filled capacitor is connected in series with a 270ohm resistor to a

Question

A large air-filled capacitor is connected in series with a 270ohm resistor to a 3000V power supply. The capacitor consists of two square plates, each 2.0m x 2.0m separated by 0.5mm

a)If the air in the capacitor breaks down and allows a spark across the gap when the electric field inside reaches 3.0*106 N/C what is the potential difference between the capacitor plates when this happens?

b) What is the conventional current in the resistor just before the spark?

A large air-filled capacitor is connected in series with a 270ohm resistor to a 3000V power supply. The capacitor consists of two square plates, each 2.0m x 2.0m separated by 0.5mm a)If the air in the capacitor breaks down and allows a spark across the gap when the electric field inside reaches 3.0*106 N/C what is the potential difference between the capacitor plates when this happens? b) What is the conventional current in the resistor just before the spark? c) How much time does it take after the power supply is connected before spark forms?

Explanation / Answer

Note that

V = Ed

As d = 0.5 mm = 0.5E-3 m, E = 3.0E6 N/C,

V = 1500 V   [ANSWER]

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As 1500 V went to the capacitor, then 3000 - 1500 V = 1500 V went to the resistor.

As V = IR --> I = V/R,

I = 1500 V / 270 ohm

= 5.556 A   [ANSWER]

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Note that

VR = Vo e^(-t/RC)

As VR = 1500 V, Vo = 3000 V, R= 270 ohm, and

C = Eo A /d

And A = s^2. Thus,

C = 7.08E-14 F

Then, plugging these in and solving for t,

t = 1.325*10^-11 s   [ANSWER]

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