Question

Explain both the laws of Kirchhoff of electrical circuits.

Hint:

Kirchhoff's laws are essential tools in solving complex electrical circuits involving multiple branches and loops.

Answer 1

Kirchhoff’s First Law (Junction Rule):
Kirchhoff's first law states that the total current entering a junction (or node) in an electric circuit is equal to the total current leaving the junction.
This law is based on the principle of conservation of electric charge.
\[ \sum I_{\text{in}} = \sum I_{\text{out}} \] Where:
- \( I_{\text{in}} \): Current flowing into the junction
- \( I_{\text{out}} \): Current flowing out of the junction
Kirchhoff’s Second Law (Loop Rule):
Kirchhoff’s second law states that the algebraic sum of the potential differences (voltages) in any closed loop or mesh of a circuit is always zero.
This law is based on the conservation of energy.
\[ \sum E = \sum IR \] Where:
- \( E \): Electromotive force (emf)
- \( I \): Current flowing through elements of the loop
- \( R \): Resistance in each segment of the loop
This means that the total energy supplied in a closed loop is equal to the total energy used.