# What is an example of an RC circuit practice problem?

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*Sample practice problem* -A08

A resistor #R=10Omega# is connected with #20muF and 10muF# capacitors and a #10V# DC battery as shown below. Analyze the circuit to find

1. Current in the loop after three time constants

2. Steady state energy stored in each capacitor.

*Sample practice problem* -A08

A resistor

1. Current in the loop after three time constants

2. Steady state energy stored in each capacitor.

##### 1 Answer

Equivalent capacitance

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

Time constant

Current

#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#

- Current after three time constants is
#I=I_0e^(-(3tau)/tau)#

#=>I=1xxe^(-3)#

#=>I=0.05A# - 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

#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#