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Multi Plate Variable Capacitor Can anyone help me?
Please can some one kindly help me with a little problem.
The construction of a multi plate variable capacitor having 4 pairs of plates. The plates when closed are separated in air by 0.01 mm and a capacitance range of 10 to 400pF is required.
a) Estimate the required radius of each plate
b) The capacitor is set to the maximum 400pF and is charged to 10V through a 50K ohm resistor. Determine (i) the initial value of the current flowing (ii) the time constant of the circuit.
Part a)
4 pairs of plates (8 plates) act like 7 capacitors in parallel.
Each plate can be estimated to be a half circle.
This site gives the formula for capacitance of one of the capacitors. Multiply by 7 for your case. Set equal to 400 pF. Solve for area per plate. Then solve for radius R.
http://www.cartage.org.lb/en/themes/sciences/physics/Electromagnetism/Electrostatics/Capacitors/Capacitors/Combination/ExampleMulti/ExampleMulti.htm
Regarding the 10 pf, there will be some stray capacitance, and if not enough, the plates can be designed not to separate completely.
Part b)
This problem is a standard RC charging problem.
Initial current = V/R = 10V/50Kohm = 0.2mA
Time constant = R x C
= 50x10^3ohm x 400x10^(-12)F = 20 us (microsecond)
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