The document describes the mesh current method for solving circuits. It begins by explaining how to mark independent meshes in a circuit and write Kirchhoff's voltage law (KVL) equations for each mesh. It then provides examples of applying the mesh current method to solve for unknown currents in different circuits, including ones with dependent sources. The examples show setting up the KVL equations for each mesh and solving the system of equations to find the mesh and other branch currents.

1. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 1
Mesh Current Method:
Mark different currents in all the independent meshes
of the given network
Current directions are arbitrary
Write KVL equations for these independent meshes
Solve for the currents
Note: Independent Meshes: Meshes having at least one new
element which is not included in the previous meshes selected.

2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2
Mesh Current Method:
For the circuit shown, determine the mesh currents i1 ,i2 and current
through the galvanometer
i2
+ -
G
4 0
2 0
3 0
3 0
1 0
RG=100
1 0 V
A
B
i 1
i 3
M1: 40 (i1) + 100 (i1 - i2) + 20 (i1 – i3) = 0
M2: 30 (i2) + 30 (i2 – i3) + 100 (i2 – i1) = 0
M3: 10 (i3) + 20 (i3 – i1) + 30 (i3 – i2) = 10
Ans: i1 = 0.10197A, i2 = 0.11184A. iG = 9.88 mA

3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3
For the circuit shown, determine the current through the 3 ohm resistor
7 V
7 A
1 Ω
1 Ω
2 Ω
2 Ω
3 Ω
i 1
i 2
i 3
1(i1-i2) + 3(i3-i2) + 1 (i3) = 7
1(i2-i1) + 2 (i2) + 3 (i2-i3) = 0
(i1 – i3 )= 7
Ans: Current through 3 ohm resistor = i2 – i3 = 0.5 A (right to left)

4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4
Mesh Equations - dependent sources
For the circuit shown determine the mesh currents
i1
i2
i3
8 V 3 Ω
2 V a
1 Ω
1 6 i b2 4 V
4 Ω
2 Ω
V a
5 Ω
i b
33 3iV&ii
circuit,theFrom
ab ==










3
2
1
i
i
i










−−
−−
−
214
1182
1226










−8
0
24
=
Ans: i1 = 2.082 A i2 = 2.386 A i3 = 1.357 A