Kirchhoff’s Current Law | Junction Rule | Kirchhoff's Point Law

Kirchhoff Current Law

Kirchhoff current law is stated as:

“In any Electrical Network, the algebraic sum of the currents meeting at a point or a junction is equal to zero”.

In Simple words it means that the total amount of current leaving a junction is equal to the total amount of the current entering the same junction.This is because of that there is no accumulation of charge at the junction of the network.Kirchhoff current law is also called a Kirchhoff Point Law and junction rule.

Assume that some conductors meeting at a point A as shown in figure 1(a).Some conductors  having currents leading to the point A and some have currents that are leading away from point A.Now Assume that the incoming currents are positive and the outgoing currents are negative,Then we have :

Incoming Currents = Outgoing Currents

 Similarly in Figure1(b) for node A

Thus the result is

KCL With the Help of Example:

Example 2.14.  In the network of Fig. 2, the different currents and voltages are as under :

                                i₂ = 5e^−2t, i₄ = 3 sin t and v₃ = 4e ^−2t

Using KCL, find voltage v₁.

Solution.  According to KCL, the algebraic sum of the currents meeting at juncion A is zero i.e.

i₁ + i₂ + i₃ + (−i₄)    = 0

i₁ + i₂ + i₃ −i₄         = 0                                                  ….(1)

Now, current through a capacitor is given by i = C dv/d

Substituting this value in Eq (1) above, we get

i₁ + 5e^−2t −16e^−2t −3 sin t = 0

or                    i₁     = 3 sin t + 11e^−2t

The voltage v₁ developed across the coil is:

  V1=L.di₁=4. di₁ (3 sin t +11e^{− 2t})

              dt       dt           

V₁ = 4 (3 cos t −22e^−2t) = 12 cos t −88e^−2t