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

Example #1

Problem:

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

DATA:
**V**_{a}*
= 12 V***, V**_{b}*
*=

Solution:

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

One can then reduce the problem to
"2 equations 2 unknowns" by substituting for *i*_{1} and obtaining 2 new equations.

One can add these two equations together to
eliminate the the *i*_{3 }term since all three resistors are the same, which
will be now noted by *R*.

Once
**i**_{2 }is
known, Eq. (4) can be used to get **i**_{3}
and **i**_{1 }can
be found by summing **i**_{2}*
*+

**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has been replaced by **Q**_{1}*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*