Question

A simple RC circuit has a resistance R = 1000 Ω and a capacitance C = 3000 µF, the capacitor is flat.

a) Determine the time required for the capacitor to charge up to 70% of the maximum charge.

b) Calculate the time necessary for the capacitor to discharge up to 50% of its initial charge.

Answer 1

For RC Circuit time constant T = RC

T=1000*3000*10^-6 = 3

Charging voltage equation can be given as

Vc = E(1-e^-t/T​​​​​​)

Current will decrease exponentially while charging

Ic = i e^{​​​​-t/T}

⁽¹⁾ 70 % of charge = 0.7 E

So 0.7E = E (1-e^-t/T)

e^{​​​​ - t/ 3} = 1-0.7

t = -3* ln 0.3

= 3.6119 sec

So it will take 3.6119 sec to charge upto 70%

(2)for discharging of capacitor

V(t) = V e ^{-t/ RC}

.5 V = V e ^-t/3

t = - ln(0.5)* 3

= 2.0794 sec

So it will take 2.0794 sec to discharge to 50% of initial charge.