Kirchhoff Law

Law1. In any network of conductors, the algebraic sum of the currents meeting at any point is zero i.e., ∑I = 0

In the above equation, current flowing into a junction is regarded as positive, while the current flowing out of the junction is regarded as negative. According to sign convention, I1, I2, I5 are positive and I2, I4, I6 are negative. Then, I₁ + I₂ – I₃ – I₄ + I₅ – I₆ = 0 i.e., I₁ + I₂ + I₅ = I₃ + I₄ + I₆

Thus the sum of currents entering the point O is equal to the sum of currents leaving it. In other words Kirchhoff’s law first law states, “When steady current flows in a electric circuit, there is no accumulation of charge at any point or junction.“


Law2. The algebraic sum of the products of the current and resistance in any closed loop of a circuit is equal to the algebraic sum of electromotive forces acting in that loop. ∑ IR = ∑ E.

Sign convention. (i) A product of current and resistance is taken as positive when we traverse in the direction of the current.

(ii) The emf is taken as positive when we traverse from the negative to the positive electrode of the cell through the electrolyte.

Let i₁ and i₂ be the currents through R1 and R2. Applying first law to the junction A, the current through R is i₁ + i₂. Then applying the second law for the closed loop ZAYZ,

i₁R₁ + (i₁ + i₂)R = E₁

Similarly, for the closed loop XAYX.

i₂R₂ + (i₁+i₂) R = E₂

For the closed loop ZAXYZ,.

I₁R₁ – i₂R₂ = E₁ – E₂

These ‘Loop equations’ enable us to obtain the values of currents in different parts of the circuit in terms R, R₁, E₁ and E₂.