 ## 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 nth branch; and in is the nth branch current leaving or entering a node
Convention: current entering a node is positive; while leaving a node is negative

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 ΙT.

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 vm is the mth 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.

Solution:

Example: Find out V1 and V2 using KVL.

Solution:

We observe that answers in both examples are handled well by polarity changes.