What is an example of an RC circuit practice problem?

Equivalent capacitance #C# of both capacitors connected in series is

#C_T=(C_1xxC_2)/(C_1+C_2)=(20xx10)/(20+10)=200/30=6.bar6muF#

Time constant #tau# of the circuit #RC=(10)(6.bar6xx10^-6)=6.bar6xx10^-5s#
Current #I# in the circuit is given by the expression

#I=I_0e^(-t/tau)#
where #I_0# is the initial current in the loop as the switch is closed.

#I_0=varepsilon/R=10/10=1A#

1. Current after three time constants is

   #I=I_0e^(-(3tau)/tau)#
   #=>I=1xxe^(-3)#
   #=>I=0.05A#

2. We know that
   #C_T=Q/varepsilon#
   #=>Q=6.bar6xx10^-6xx10=6.bar6xx10^-5C#

In the steady state there is no current flowing in the loop. Hence, voltage drop across resistor #=0#. Voltage of battery is divided across capacitors in the inverse fraction of respective capacitances.

#V_10=varepsilonxxC_T/C_10=10xx(6.bar6)/10=6.bar6V#

The balance voltage appears across other capacitor.

#:.V_20=10-6.bar6=3.bar3V#

Now energy stored in a capacitor is given by the expression

#E=1/2CV^2#
#:.E_10=1/2xx(10xx10^-6)(6.bar6)^2#
#=>E_10=2.bar2xx10^-4J#

Similarly

#E_20=1/2xx(20xx10^-6)(3.bar3)^2=1.bar1xx10^-4J#