Question

In an RC series circuit, V = 24.0 V, resistance R = 47 K?, and capacitance C = 2200 ?F.

(a) Calculate the time constant.

(b) Define time constant in a complete sentence.

(c) How long does it take for the capacitor to reach to its 63% of its maximum charge?

(d) How long does it take for the capacitor to reach to its 75% of it maximum charge?

(e) How much charge can be stored in the capacitor after 50 seconds?

Please show all steps thank you!

Answer 1

battery, V=24 v

resistance, R=47*10^3 Ohms

capacitance, C=2200*10^-6 F

a)

time constant, t=R*C

t=47*10^3*2200*10^-6

t=103.4 sec

b)

time required to charge the capacitor to 63% of the maximum charge

c)

if q=63% of qo

==> q=0.63*qo

q=qo*(1-e^-t/T)

0.63*qo=qo*(1-e^(-t/103.4))

0.63=(1-e^(-t/103.4))

t=103 sec

d)

if q=75% of qo

==> q=0.75*qo

q=qo*(1-e^-t/T)

0.75*qo=qo*(1-e^(-t/103.4))

0.75=(1-e^(-t/103.4))

t=143.34 sec

e)

at t=50 sec

q=qo*(1-e^-t/T)

q=C*V*(1-e^-t/T)

q=2200*10^-6*24*(1-e^(-50/103.4))

q=20.24*10^-3 C

or q=20.24 mC