A 5.0 F capacitor is charge to a potential difference of 20 kV between plates. A

Question

A 5.0 F capacitor is charge to a potential difference of 20 kV between plates. After being disconnected from the power source, it is connected across a 7.0 M resistor to discharge.

(i)

What is the initial discharge current?

(ii)

Calculate the time constant of the circuit.

A 670 F capacitor is charged together with a resistor of
100 k in series through a potential difference of 2.5 V between plates.

Calculate the time constant of the circuit.

(2 marks)

(ii)

Find the half-life of the circuit.

(2 marks)

(iii)

At t = 40 s, calculate the voltage across the capacitor.

(3 marks)

(iv)

Find time needed to charge the capacitor to 2.0 V.

(3 marks)

A 5.0 F capacitor is charge to a potential difference of 20 kV between plates. After being disconnected from the power source, it is connected across a 7.0 M resistor to discharge.

(i)

What is the initial discharge current?

(ii)

Calculate the time constant of the circuit.

Explanation / Answer

i)

Initial Discharge current = 20*1000/7000 = 2.857 A

ii)

Time constant of circuit is

T =RC =7*1000*5*10^-6 = 0.035 seconds

2)

Timeconstant T =RC = 100*10^3*670*10^-6 = 67 seconds

Half Life = T*ln2 = 46.44 seconds

V=V0(1-exp(-40/67)) =2.5*(1-exp(-40/67)) = 1.125 Volts

2 = 2.5 * (1-Exp(-t/60)) calculate t

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