Fundamentals_of_Electrical_Eng. 1st by Dr. Ali Al-Hussaini >>>> Lect.3
Solving Circuits with Kirchoff Laws
Example 1: Find the three unknown currents (
voltages (
) and three unknown
) in the circuit below:
Note: The direction of a current and the polarity of a voltage source can be
assumed arbitrarily. To determine the actual direction and polarity, the sign of
the values also should be considered. For example, a current labeled in left-toright direction with a negative value is actually flowing right-to-left.
All voltages and currents in the circuit can be found by either of the following
two methods, based on either the KVL or KCL.

The loop-current method based on KVL:
1. For each of the independent loops in the circuit, define a loop
current around the loop in clockwise (or counter clockwise)
direction. These loop currents are the unknown variables to be
obtained.
2. Apply KVL around each of the loops in the same clockwise
direction to obtain equations. While calculating the voltage drop
across each resistor shared by two loops, both loop currents (in
opposite positions) should be considered.
3. Solve the equation system with equations for the unknown
loop currents.
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Fundamentals_of_Electrical_Eng. 1st by Dr. Ali Al-Hussaini >>>> Lect.3
Find currents
o
from a to b,
from c to b, and
Assume two loop currents
and
and apply the KVL to them:
from b to d.
around loops abda and bcdb
We rewrite these as:
and then get
,
and
. Having found
all voltages in the circuit.
,
and
, we can easily find
Example 3: Solve the following circuit
with
,
,
,
,
,
circuit has 3 independent loops and 3 independent nodes.
. This
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Fundamentals_of_Electrical_Eng. 1st by Dr. Ali Al-Hussaini >>>> Lect.3

Loop current method:
Assume three loop currents
direction. We have
(left),
(right),
(top) all in clock-wise
We can also get the three node voltages with respect to the bottom node
as
ground:
(right),
(middle),
and
(left).
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Fundamentals_of_Electrical_Eng. 1st by Dr. Ali Al-Hussaini >>>> Lect.3
Example 2: Solve the following circuit:

Loop current method: Let the three loop currents in the example above
be ,
and
for loops 1 (top-left bacb), 2 (top-right adca), and 3
(bottom bcdb), respectively, and applying KVL to the three loops, we get
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