KCL And KVL Explained With Solved Numericals In Detail

Kirchoff’s Current (KCL) and Voltage Laws (KVL)

Ohm’s law alone is not sufficient to analyze circuits unless it is coupled with Kirchhoff’s two laws:

Kirchoff’s Current law (KCL)
Kirchoff’s Voltage law (KVL)

KCL

KCL states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

Mathematically

Where ‘N’ is the number of branches connected to the node ‘n’ is the n^th branch; and i_n is the n^th branch current leaving or entering a node
Convention: current entering a node is positive; while leaving a node is negative

KCL equation:i₁ – i₅ + i₄+ i₃– i₂ = 0i₁ + i₃ + i₄= i₂– i₅

Alternate KCL: The sum of currents entering a node is equal to the sum of currents leaving the node.

Example: Write KCL on node ‘a’ and find out Ι_T.

Solution:

So, an application of KCL is to combine current sources in parallel into one equivalent current source.

A circuit cannot contain two different currents Ι₁ and Ι₂ in series unless Ι₁=i₂; otherwise KCL will be violated.

KVL:

KVL states that the algebraic sum of all voltage around a closed path (or loop) is zero.

Mathematically,

Where M is the no. of voltages in a loop (or the number of branches in a loop), and v_m is the m^th voltage.

Convention: The sign on each voltage is the polarity of the terminal encountered first as we travel around the loop.
Example:

Alternate KVL: The sum of voltage drops is equal to the sum of voltage rises.

Example: Apply loop in the following circuit and find out Vab:

This is an application of KVL where the voltage source in series can be combined into one equivalent source.
Note that a circuit cannot contain two different voltages V1 and V2 in parallel unless V1 = V2; Otherwise KVL would be violated.

Example: Find out V₁ and V₂ using KVL.