DC Network Theorems - Kirchhoffs Laws

DC Network Theorems – Kirchhoffs Laws

These laws are more comprehensive than Ohm’s law and are used for solving electrical networks which may not be readily solved by the latter.

Kirchhoff's Current Law OR Kirchhoff's Point Law :

Kirchhoff’s Current Law

In any electrical network, the algebraic sum of the currents meeting at a point (or junction) is zero.

Put in another way, it simply means that the total current leaving a junction is equal to the total current entering that junction. It is obviously true because there is no accumulation of charge at the junction of the network.

Consider the case of a few conductors meeting at a point A as in Figure given below. Some conductors have currents leading to point A, whereas some have currents leading away from point A. Assuming the incoming currents to be positive and the outgoing currents negative, we have

I₁ + (− I₂) + (− I₃) + (+ I₄) + (− I₅) = 0
or I₁ + I₄ − I₂ − I₃ − I₅ = 0 or I₁ + I₄ = I₂ + I₃ + I₅

or incoming currents = outgoing currents

Similarly, in Figure given below for node A
+ I + (− I₁) + (− I₂) + (− I₃) + (− I₄) = 0 or I= I₁ + I₂ + I₃ + I₄
We can express the above conclusion thus : Σ I = 0 ……………….at a junction

2. Kirchhoff’s Mesh Law or Voltage Law (KVL)

It is Second Law :
The algebraic sum of the products of currents and resistances in each of the conductors in any closed path (or mesh) in a network plus the algebraic sum of the e.m.fs. in that path is zero.

In other words, Σ IR + Σ e.m.f. = 0 ……round a mesh

It should be noted that algebraic sum is the sum which takes into account the polarities of the voltage drops.

The basis of this law is this : If we start from a particular junction and go round the mesh till we come back to the starting point, then we must be at the same potential with which we started. Hence, it means that all the sources of e.m.f. met on the way must necessarily be equal to the voltage drops in the resistances, every voltage being given its proper sign, plus or minus.

Read article – Units of Resistivity

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