Kirchhoff Voltage Law

Kirchhoff Voltage Law

This law deals with the voltage drops at various branches in an electrical circuits. Think about one point on an closed loop in an electrical circuit. If some one goes to any other point on the same loop, he or she will find that the potential at that second point may be different from first point. If he or she continues to go to some different point in the loop, he or she may find some different potential at that new location. If he or she goes on further along that closed loop ultimately he or she reaches the initial point from where the journey was started. That means he or she comes back to the same potential point after crossing through different voltage levels. It can be alternatively said that net voltage gain and net voltage drops along a closed loop are equal. That is what Kirchhoff Voltage law states. This law is alternatively known as Kirchhoff Second Law.

If we consider a closed loop, conventionally if we consider all the voltage gains along the loop are positive then all the voltage drops along the loop should be considered as negative. The summation of all these voltages in a closed loop is equal to zero. Suppose n numbers of back to back connected elements form a closed loop. Among these circuit element m number elements are voltage source and n – m number of elements drop voltage such as resistors.

The voltages of sources are V1, V2, V3,………………. Vm

and voltage drops across the resistors respectively, Vm + 1,
Vm + 2, Vm + 3,………………… Vn.

As it said that the voltage gain conventionally considered as positive, and voltage drops are considered as negative, the voltages along the closed loop are

+ V1, + V2, + V3,………………. + Vm, − Vm + 1, − Vm + 2, − Vm + 3,…………………− Vn.

Now according to Kirchhoff Voltage law the summation of all these voltages results to zero.

That means, V1 + V2 + V3 + ………………. + Vm − Vm + 1 − Vm + 2 − Vm + 3 + …………………− Vn = 0

So accordingly Kirchhoff Second Law, ∑V = 0