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## Homework Statement

A multi plate variable capacitor has 4 pair of plates. The plates, when closed, are separated in air by 0.01mm and a capacitance range of 10 to 400pF.

a) Estimate the required radius R of each plate.

b) The capacitor is set to maximum 400pF and is charged to 10V through a 50kΩ resistor. Determine:

i) The initial value of the current flowing.

ii) The time constant for the circuit.

## Homework Equations

C = εr εo A (n-1)/d

## The Attempt at a Solution

I am still new to all this so please dont go too technical with any replies.

I think the correct formula to work out the radius is C=εr εo A (n-1)/d

Transpose this to make A the subject:

A= Cd/εr εo (n-1)

Which gives me A= (400x10^-12)x(0.00001)/1 x 8.85x10^-12 x 7

Area of plate = 0.00316 (I think this is meter^2)

Then use this answer in A=∏r^2

Transpose for radius = √A/∏

Which gives me an answer of 0.0317 (Again I think this is meters).

bi) The initial value of current flowing.

If t=0 The charging current has its highest value.

Therefore io=V/R

=10/50000

=0.0002 Amps

bii) The time constant t=CR

t=(400x10^-12)x 50000

t=0.00002s

Could you tell me if I am going about these the correct way or am I way off mark thanks.