Kirchhoff's Laws Study Notes for SSC JE & Other AE JE Exams

Kirchhoff's Law

Kirchhoff’s current law (KCL):

KCL states that the algebraic sum of the currents entering a node or meeting at a point is zero.

→ It is based on law of conservation of charge.

               Figure 1

⇒I₁ + I₂ + (– I₃) + I₄ + (– I₅) = 0

Incoming current consider as Positive

Outgoing current consider as Negative.

Kirchhoff’s voltage law(KVL):

It states that algebraic sum of all the voltages in a closed loop is zero.

It is based on the law of conservation of energy.

                 Figure 2

– V_s + IR₁ + IR₂ = O

Rise in potential = negative, Fall in potential = positive (or) vice-versa.

Mesh Analysis

Mesh is a loop which cannot contain any inner loop.

It is applicable only for the planner network and a planner network is that can be drawn in a plane with no branches crossing are another.

                           Figure 3

Loops → L₁, L₂, L₃

Mesh → L₁, L₂

Procedure:

• Identify the total number of meshes.
• A sign the mesh current
• Develop KVL equation for each mesh.
• Solve equation to find the loop current.

Note: Number of equations required to solve the circuit with the help of mesh analysis are:

Where,

b = number of branches

N = number of nodes

Nodal Analysis

Procedure:

• identify total number of nodes in the circuit.
• Assign the voltage at each node and one of the nodes is taken as the reference node and the potential of reference node is equal to the ground potential.
• Develop KCL equation for each non – reference node.
• By solving KCL equation, find the node voltages.

 The total number of equations required to solve the network by using nodal analysis are:

e=N-1

Way of writing equation at a node:

                                                Figure 4

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