Question

A 3.0M? resistor is connected in series with an initially uncharged 0.27?F capacitor. This arrangement is then connected across four 1.5-V batteries (also in series).

A)

What is the maximum current in the circuit?

B)

When does it occur? (sec)

C)

What percentage of the maximum current is in the circuit after 1.4s

D)

What is the maximum charge on the capacitor?

E)

When does it occur? (sec)

F)

What percentage of the maximum charge is on the capacitor after 1.4s ?

G)

How much energy is stored in the capacitor after one time constant has elapsed? (J)

Answer 1

A)

this is simple RC circuit

voltage across the capacitor

V_C=V(1-exp(-t/RC))

=1.5(1-exp(-t/0.81)

I=C.dv/dt

=c*1.5/0.81 *exp(-t/0.81)

=0.5*10^-6*exp(-t/0.81)

maximum current flows through the circuit

when t=0

I_max=0.5*10^-6A

C)

at 1.4 seconds

I=0.08*10^-6

percentage of maximum current

=0.08/0.5

=16%

D)

maximum charge

Q_max=CV_max

=0.27*10^-6*1.26

=0.3402*10^-6

T=5timeconstants

F)

Q=0.27*/10^-6*1.5*(1-exp(-1.4/0.81))

=0.333*10^-6

G)

E=0.5CV²

=0.5*0.27*10^-6*1.233

=0.1664j