**Kirchoffâ€™s Current (KCL) and Voltage Laws (KVL)**

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

- Kirchoffâ€™s Current law (KCL)
- Kirchoffâ€™s Voltage law (KVL)

__KCL__

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

Where â€˜Nâ€™ is the number of branches connected to the node â€˜nâ€™ 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: 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: **Write KCL on node â€˜aâ€™ 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}and Î™_{2}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), 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 *V*_{1} and *V*_{2} 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.

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