Mesh Analysis Made Easy: 40 MCQs + Viva + Supermesh
Tricks (Last-Minute Exam Notes)
Introduction
Mesh Analysis (also known as Loop Analysis) is one of the most powerful and systematic
techniques used in electrical engineering to analyze planar circuits. Based on Kirchhoff’s
Voltage Law (KVL), this method allows us to determine unknown currents in a circuit by
assigning mesh currents to independent loops.
This document is designed as a complete exam-focused guide to help students quickly
understand and apply mesh analysis with confidence. It covers fundamental concepts, matrix
methods, and advanced topics like supermesh in a simple and structured way.
To make your preparation more effective, this note also includes:
✔ 40 carefully selected MCQs for practice
✔ Viva questions with clear answers
✔ Supermesh shortcuts and problem-solving tricks
✔ Common mistakes to avoid in exams
✔ A quick revision sheet for last-minute study
Whether you are preparing for university exams, viva, or competitive tests, this material will
help you revise faster, solve problems efficiently, and score higher marks.
Last-Minute Revision Sheet
KVL formula
Matrix structure
Supermesh steps
Key formulas:
o Self resistance = sum
o Mutual resistance = negative sum
Common Exam Mistakes
❌ Forgetting negative sign in shared resistance
❌ Not applying KCL in supermesh
❌ Taking wrong loop direction
❌ Including current source in KVL
Mesh Analysis (or Loop Analysis or Mesh Current Method)
Let us consider the network shown in Figure 1. It consists of three loops [Loop (I), loop (II)
and loop (III)]. The three loop currents are i1, i2 and i3 and they are assumed to flow in a
clockwise direction. Here, the currents in different loops are assigned continuous paths so
that they do not split at a junction into branch currents. The mesh analysis or loop analysis is
1
, based on Kirchhoff’s voltage law (KVL). Here in this method three loop currents i1, i2 and i3
are unknown quantities.
Apply KVL in loop (I) in clockwise direction,
V1 i1 R1 i1 i2 R2 0
i1 R1 R2 i2 R2 V1.................................(i )
Apply KVL in loop (II) in clockwise direction,
i2 R3 i2 i3 R4 i2 i1 R2 0
i1 R2 i2 R2 R3 R4 i3 R4 0........(ii )
Apply KVL in loop (III) in clockwise direction,
i3 R5 V2 i3 i2 R4 0
i2 R4 i3 R4 R5 V2 ............................(iii )
Solving equations (i), (ii) and (iii), we can find the values of i1, i2 and i3.
Equations (i), (ii) and (iii) can be written in matrix form as
R1 R2 R2 0 i1 V1
R2 R2 R3 R4 R4 i2 0 .......................(iv)
0 R4 R4 R5 i3 V2
In general, the resistance matrix [R] can be written as
R11 R12 R13
R R22 R23 ........................................(v)
21
R31 R32 R33
Where
R11=self resistance of loop (I)=R1+R2
R22=self resistance of loop (II)=R2+R3+R4
R33=self resistance of loop (III)=R4+R5
R12=R21= -[sum of all the resistances common to loops (I) and (II)] = -R2
2
Tricks (Last-Minute Exam Notes)
Introduction
Mesh Analysis (also known as Loop Analysis) is one of the most powerful and systematic
techniques used in electrical engineering to analyze planar circuits. Based on Kirchhoff’s
Voltage Law (KVL), this method allows us to determine unknown currents in a circuit by
assigning mesh currents to independent loops.
This document is designed as a complete exam-focused guide to help students quickly
understand and apply mesh analysis with confidence. It covers fundamental concepts, matrix
methods, and advanced topics like supermesh in a simple and structured way.
To make your preparation more effective, this note also includes:
✔ 40 carefully selected MCQs for practice
✔ Viva questions with clear answers
✔ Supermesh shortcuts and problem-solving tricks
✔ Common mistakes to avoid in exams
✔ A quick revision sheet for last-minute study
Whether you are preparing for university exams, viva, or competitive tests, this material will
help you revise faster, solve problems efficiently, and score higher marks.
Last-Minute Revision Sheet
KVL formula
Matrix structure
Supermesh steps
Key formulas:
o Self resistance = sum
o Mutual resistance = negative sum
Common Exam Mistakes
❌ Forgetting negative sign in shared resistance
❌ Not applying KCL in supermesh
❌ Taking wrong loop direction
❌ Including current source in KVL
Mesh Analysis (or Loop Analysis or Mesh Current Method)
Let us consider the network shown in Figure 1. It consists of three loops [Loop (I), loop (II)
and loop (III)]. The three loop currents are i1, i2 and i3 and they are assumed to flow in a
clockwise direction. Here, the currents in different loops are assigned continuous paths so
that they do not split at a junction into branch currents. The mesh analysis or loop analysis is
1
, based on Kirchhoff’s voltage law (KVL). Here in this method three loop currents i1, i2 and i3
are unknown quantities.
Apply KVL in loop (I) in clockwise direction,
V1 i1 R1 i1 i2 R2 0
i1 R1 R2 i2 R2 V1.................................(i )
Apply KVL in loop (II) in clockwise direction,
i2 R3 i2 i3 R4 i2 i1 R2 0
i1 R2 i2 R2 R3 R4 i3 R4 0........(ii )
Apply KVL in loop (III) in clockwise direction,
i3 R5 V2 i3 i2 R4 0
i2 R4 i3 R4 R5 V2 ............................(iii )
Solving equations (i), (ii) and (iii), we can find the values of i1, i2 and i3.
Equations (i), (ii) and (iii) can be written in matrix form as
R1 R2 R2 0 i1 V1
R2 R2 R3 R4 R4 i2 0 .......................(iv)
0 R4 R4 R5 i3 V2
In general, the resistance matrix [R] can be written as
R11 R12 R13
R R22 R23 ........................................(v)
21
R31 R32 R33
Where
R11=self resistance of loop (I)=R1+R2
R22=self resistance of loop (II)=R2+R3+R4
R33=self resistance of loop (III)=R4+R5
R12=R21= -[sum of all the resistances common to loops (I) and (II)] = -R2
2
