Kirchoff’s law is named after German physicist Gustav Rober Kirchhoff, and it consists of two fundamental laws of electricity, which makes circuit analysis of complex circuits easy.

Kirchhoff’s first law or current law states that the sum of currents entering any junction of a circuit should always be equal to the sum of the currents leaving the same junction.

Sum of currents entering the junction = Sum of currents leaving the same junction
$\implies $ ∑ I _In = ∑ I _Out
$\implies $I₁ + I₂ + I₃ = I₄ + I₅
Kirchhoff’s current law is the direct consequence of conservation of charge. Using this law, we can derive the formula for the combined resistance of two or more resistors in parallel.

$\frac{\text{1}}{\text{R}_{1}} = \frac{\text{1}}{\text{R}_{1}} + \frac{\text{1}}{\text{R}_{2}} + \frac{\text{1}}{\text{R}_{3}}$

If more resistors are added in parallel, the combined resistance goes on decreasing. Also, the combined resistance of a parallel combination is always smaller than the smallest individual resistance.

Kirchhoff’s second law or voltage law states that the algebraic sum of potential differences, or the change in potential in any loop must be zero.

Algebraic sum of potential differences around a loop =
∑ V = 0
$\implies$ -IR₁ + (-IR₂) +(-IR₃) +E₁ +E₂ = 0
$\implies$ E₁ +E₂ = IR₁ + IR₂ + IR₃

Kirchhoff’s voltage law is a direct consequence of conservation of energy. Using this law, we can derive the formula for the combined resistance of two or more resistors in series.

R = R₁ + R₂ +R₃

If more resistors are added in series, the combined resistance goes on increasing. Also, the combined resistance of a series combination is always greater than the greatest individual resistance.

10.03 - Kirchhoff’s Law

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