**Kirchoffâs Current (KCL) and Voltage Laws (KVL)**

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

- Kirchoffâs Current law (KCL)
- Kirchoffâs Voltage law (KVL)

__KCL__

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

Where âNâ is the number of branches connected to the node ânâ is the n^{th}Â branch; andÂ *i _{n}*Â is the n

^{th}Â branch current leaving or entering a node

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**Â Convention:**current entering a node is positive; while leaving a node is negative

KCL equation: i â _{1}i +_{5} i+_{4 } iâ_{3 } i = 0_{2}i + _{1}i +_{3} iâ_{4 }= i_{2 } i _{5} |

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

**Example:Â **Write KCL on node âaâ and find out Î_{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 Î
_{1}Â and Î_{2}Â in series unless Î_{1}=i_{2}; otherwise KCL will be violated.

__KVL:__

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

Where M is the no. of voltages in a loop (or the number of branches in a loop), Â andÂ *v*_{m}Â is the m^{th}Â voltage.

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

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

**Example**: Â 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:Â **Find outÂ *V*_{1}Â andÂ *V*_{2}Â using KVL.

**Solution:**

**Example: **Find out *V*_{1} and *V*_{2} using KVL.

**Solution:**

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