Kirchhoffs first rule

Kirchhoff’s first rule also called the rule of junction point states that the electric current that enters a junction point is the same as the electric current exit from that junction point. The junction point in an electrical circuit is the point where two or more of the two conductors meet, such as point a in the figure on the side.

I is the electric current that enters the junction point, while I₁ and I₂ are the electric currents that exit from the junction point, I = I₁ + I₂. Another example, observe the figure below.

I is the incoming electric current, while I₁, I_2, and I₃ are the outgoing electric currents, I = I₁ + I₂ + I₃.

Kirchhoff’s first rule is based on the conservation law of electric charge which states that the charge is eternal, the incoming electric charge must be equal to the electric charge that comes out, no electrical charge is lost. Electric current is an electric charge that flows during a certain time interval. The electric current that enters a junction point is the same as the electric current coming out from that junction point.

Kirchhoff’s first rule stated by Gustav Kirchhoff (1824-1887), a German physicist.

Sample problem 1:

I₁ = 2 A, I₂ = 3 A, I₃ = 5 A, I₄ = 3 A. Determine I₅!

Solution:

I enter = I exit

I₁ + I₃ = I₂ + I₄ + I₅

2 A + 5 A = 3 A + 3 A + I₅

7 A = 6 A + I₅

I₅ = 7 A – 6 A

I₅ = 1 A

Sample problem 2:

I = 10 A, I₁ = 2 A, I₂ = 4 A. Determine I₃!

Solution:

I enter = I exit

I = I₁ + I₂ + I₃

10 A = 2 A + 4 A + I₃

10 A = 6 A + I₃

I₃ = 10 A – 6 A

I₃ = 4 A