Lecture๎Twelve๎
Loop๎(Mesh)๎Analysis๎
Independent๎Voltage๎Sources๎
Problem๎Solving๎Strategy๎
1. Identify๎loops๎(starting๎from๎one๎node,๎traverse๎the๎circuit๎element๎once๎until๎we๎reach๎
that๎node๎again๎is๎called๎loop๎or๎mesh)๎
2. For๎each๎loop๎in๎the๎network,๎specify๎the๎direction๎of๎loop๎currents.๎The๎direction๎of๎all๎
loop๎currents๎should๎be๎same๎i.e.๎either๎clockwise๎or๎counterโclockwise.๎
3. ๎Write๎N๎KVL๎equations๎for๎N๎loops.๎
4. Solve๎simultaneously๎to๎evaluate๎loop๎currents.๎
Example๎
Write๎the๎mesh๎equations๎for๎the๎circuit๎below:๎
11 1 2 3 12 1
11 2 3 23 1
24 25 2 1 3 1
13 2 3 4 5 1
1: ( )
()
2: ( )
()
s
s
s
s
loop I R I I R I R V
IR R R IR V
loop IR IR I I R V
I
RIRRR V
+โ + =
โ++โ=
++โ =โ
โโ + + + =โ
๎
Or๎in๎matrix๎form๎
123 3 1
1
3345 1
2
1
s
s
RRR R V
I
R
RRR V
I
โ
++ โ
โกโคโกโค
โกโค
=
โขโฅโขโฅโขโฅ
โ++ โ
โฃโฆโฃโฆโฃโฆ
=
RI = V
IRV
๎๎
Example:๎
Write๎loop๎equations๎for๎the๎network๎shown:๎
11 1 2 2 1 2
212 232425 3
1: ( )
2:( )
ss
s
loop I R I I R V V
loop I I R I R I R I R V
+โ =+
โ+++=โ
๎
๎
๎
๎
๎
๎
๎
๎
๎
Vs3
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