Question

What is Kirchhoff's Current Law (KCL) ?

Answer 1

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Understanding Kirchhoff's Current Law (KCL): Definition, Formula, and Example

Kirchhoff's Current Law, often abbreviated as KCL, is a fundamental principle used in the analysis of electrical circuits. It provides a simple but powerful rule for understanding how current behaves at any junction point in a circuit.

What is Kirchhoff's Current Law?

Kirchhoff's Current Law states that:

"The algebraic sum of currents entering a node (or junction) in an electrical circuit is zero."

In simpler terms, this means that the total amount of current flowing into any single point in a circuit must be equal to the total amount of current flowing out of that same point. This principle is a direct result of the law of conservation of charge, which dictates that charge cannot be created or destroyed—it can only be moved. At a junction, no charge is lost or stored.

The KCL Formula

KCL can be expressed mathematically in two common ways:

1. Sum of Currents In = Sum of Currents Out: This is the most intuitive form of the law.
   Σ I_in = Σ I_out

2. Using Sign Convention: By assigning a positive sign to currents entering a node and a negative sign to currents leaving (or vice-versa), the law can be written as:
   Σ I = 0

As shown in the image, this can be summarized as:
CURRENTS ENTERING THE NODE EQUALS CURRENT LEAVING THE NODE

KCL Example: Solving for an Unknown Current

Let's walk through the example provided in the image to see how KCL is applied.

Diagram:
The circuit diagram shows a central point, labeled Node, where five different paths for current meet.
Currents I₁ and I₂ are flowing into the node.
Currents I₃, I₄, and I₅ are flowing out of the node.

Problem:
Given the following values, find the unknown current I₅.
I₁ = 3 A
I₂ = 2 A
I₃ = 1 A
I₄ = 2 A

Applying KCL:

1. Set up the equation: According to KCL, the sum of currents entering the node equals the sum of currents leaving the node.
   I₁ + I₂ = I₃ + I₄ + I₅

2. Substitute the known values: Plug the given current values into the equation.
   3 A + 2 A = 1 A + 2 A + I₅

3. Simplify both sides:
   5 A = 3 A + I₅

4. Solve for the unknown current (I₅): Isolate I₅ by subtracting 3 A from both sides.
   I₅ = 5 A - 3 A
I₅ = 2 A

Answer:
The value of the unknown current is I₅ = 2 A.