**Kirchoff's
laws / RC Circuits Examples**

Example #1

Problem:

Find the currents through all the resistors in the circuit below:

DATA:
**V**_{b}*
*=

Solution:

Summing the voltages around the left and right loops gives the following two equations:

where **i**_{3}
has been replaced by **i**_{1}*
*-

which rearranged yields

Once
**i**_{2 }is
known, Eq. (1) can be used to get **i**_{1},
and **i**_{3}
can be found as the difference **i**_{1}*
*-

**i**_{2}
= 0.554 amps, **i**_{1}=
.369 amps, **i**_{3 }=
-.185 amps

Example #2

Problem:

Find the charges on all the capacitors in the circuit below:

DATA:
**V**_{b}*
*=

Solution:

Summing the voltages around the left and right loops gives the following two equations

where **Q**_{3}
has been replaced by **Q**_{1}*
*-

which rearranged yields

Once
**Q**_{2 }is
known, Eq. (1) can be used to get **Q**_{1},
and **Q**_{3}
can be found as the difference **Q**_{1}*
*-

**Q**_{2}
= 120.0 m*C*, **Q**_{1}=
40.0 m*C*, **Q**_{3
}= -80 m*C*

Example #3

The circuit below
has been in position * a* for a long time.
At time

a.) What is the curnent through the resistor just BEFORE the switch is thrown?

**I*** = *0

b.) What is the current through the resistor just AFTER the switch is thrown?

Solution: **I = V/R**

**I*** = *0.6* *amps

c.) What is the charge across the capacitor just BEFORE the switch is thrown?

Solution: **Q = CV**

**Q*** = *120* **m**C*

d.) What is the charge on the capacitor just AFTER the switch is thrown?

Solution: Charge does not change instantaneously.

**Q*** = *120* **m**C*

e.) What is the
charge on the capacitor at at time * t *=

Solution: **Q = Q**_{0}**exp(-t/****t****) ,** where** ****t**** **=** RC **= 0.2 msec

**Q*** = *26.8* **m**C*

Example #4

Considering the
same circuit, only with the switch thrown from * b*
to

a.) What is the curnent through the resistor just BEFORE the switch is thrown?

**I*** = *0

b.) What is the current through the resistor just AFTER the switch is thrown?

Solution: **I = V/R**

**I*** = *0.6* *amps

c.) What is the charge across the capacitor just BEFORE the switch is thrown?

Solution: **Q = CV**

**Q*** = *0* *

d.) What is the charge on the capacitor just AFTER the switch is thrown?

Solution: Charge does not change instantaneously.

**Q*** = *0* *

e.) What is the
charge on the capacitor at at time * t *=

Solution: **Q = Q**_{0}**(1.0
- exp(-t/****t****)) ,** where** ****t**** **=** RC **= 0.2 msec

**Q*** = *93.2* **m**C*