Question

What is the KCL KVL law?

Answer 1

### Kirchhoff's Current Law (KCL)
Kirchhoff's Current Law states that **the total current entering a junction (or node) in an electrical circuit is equal to the total current leaving the junction**. This law is based on the principle of conservation of charge, meaning that no charge is lost at a junction, and current is just passing through or out of it.

**Mathematically:**
\[
\sum I_{\text{in}} = \sum I_{\text{out}}
\]
Where:
- \( I_{\text{in}} \) is the current entering the junction.
- \( I_{\text{out}} \) is the current leaving the junction.

**Example:**  
If three wires meet at a junction and the currents are \( I_1 = 5 \, A \), \( I_2 = 3 \, A \) (entering), and \( I_3 \) (leaving), KCL tells us that:
\[
I_1 + I_2 = I_3
\]
So, \( I_3 = 5 \, A + 3 \, A = 8 \, A \).

### Kirchhoff's Voltage Law (KVL)
Kirchhoff's Voltage Law states that **the sum of all voltages around a closed loop (or mesh) in a circuit is zero**. This is based on the principle of energy conservation, meaning the total energy gained per unit charge is equal to the total energy lost per unit charge in any closed loop.

**Mathematically:**
\[
\sum V = 0
\]
Where the sum of all the voltage drops and voltage gains around a loop equals zero.

**Example:**  
In a simple loop with resistors and a battery:
- If the battery provides \( 10 \, V \) and there are two resistors with voltage drops of \( 4 \, V \) and \( 6 \, V \), then:
\[
10 \, V - 4 \, V - 6 \, V = 0 \, V
\]
This confirms KVL, as the voltage gains and drops balance each other out in the loop.

### Summary:
- **KCL** deals with the currents at a junction or node (sum of currents in = sum of currents out).
- **KVL** deals with the voltages in a closed loop (sum of all voltages = 0).

Both laws are fundamental in analyzing and solving electrical circuits.