Question

State and explain Kirchhoff’s law?

Answer 1

Kirchhoff's laws are two fundamental principles used to analyze electric circuits. They were formulated by Gustav Kirchhoff in 1845 and are based on the conservation of charge and energy.

Let's break down each law, using your provided images as examples.

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1. Kirchhoff’s Current Law (KCL)

This law is also known as Kirchhoff's First Law, the Junction Rule, or the Node Law.

Statement:
The algebraic sum of all currents entering and leaving a node (or junction) in a circuit must be equal to zero. A simpler way to state this is:

The sum of currents flowing into a node is equal to the sum of currents flowing out of that node.

Explanation:
KCL is based on the principle of conservation of charge. Charge cannot be created or destroyed, so any charge that flows into a junction must immediately flow out. Think of it like water pipes connected at a junction; the amount of water flowing in per second must equal the amount of water flowing out per second, as the junction itself cannot store water.

• Node: The red dot in the center is the node or junction where multiple wires meet.
• Currents In: The arrows for currents I₁ and I₂ point towards the node.
• Currents Out: The arrows for currents I₃, I₄, and I₅ point away from the node.

According to KCL:
Sum of Currents In = Sum of Currents Out
I₁ + I₂ = I₃ + I₄ + I₅

This equation, shown at the bottom of your image, is a perfect application of Kirchhoff's Current Law.

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2. Kirchhoff’s Voltage Law (KVL)

This law is also known as Kirchhoff's Second Law or the Loop Rule.

Statement:
The algebraic sum of all the voltage rises and voltage drops around any closed loop in a circuit must be equal to zero. This can also be stated as:

In any closed loop, the sum of the voltage rises (from sources like batteries) is equal to the sum of the voltage drops (across components like resistors).

Explanation:
KVL is based on the principle of conservation of energy. Imagine moving a charge around a closed loop and returning to your starting point. The charge must have the same amount of potential energy as when it started. Any energy gained from a voltage source (a "rise" in potential) must be lost or dissipated by the components in the loop (a "drop" in potential). Think of it like hiking a mountain trail that starts and ends at the same point; the total distance you climb up must equal the total distance you descend.

• Closed Loop: The path indicated by the red arrow forms a single closed loop.
• Voltage Rise: The battery, Vs, provides energy to the circuit. As current flows from the negative (-) to the positive (+) terminal through the battery, there is a voltage rise.
• Voltage Drops: As the current flows through the resistors R₁, R₂, and R₃, energy is dissipated (usually as heat). This causes a voltage drop across each resistor, indicated by V₁, V₂, and V₃. The + and - signs show the direction of the drop, from higher potential to lower potential.

According to KVL, if we travel around the loop in the direction of the current (the red arrow):
Sum of Voltage Rises = Sum of Voltage Drops
Vs = V₁ + V₂ + V₃

Alternatively, using the "algebraic sum is zero" definition:
+Vs - V₁ - V₂ - V₃ = 0
(We gain Vs from the battery, then lose V₁, V₂, and V₃ across the resistors).

Both equations express the same fundamental relationship described by Kirchhoff's Voltage Law.

Summary

| Law | Principle | Simple Statement | Application |
| :--- | :--- | :--- | :--- |
| Kirchhoff's Current Law (KCL) | Conservation of Charge | What goes in must come out. | Used at nodes/junctions. |
| Kirchhoff's Voltage Law (KVL) | Conservation of Energy | The sum of ups equals the sum of downs. | Used for closed loops. |

These two laws are the foundation for analyzing nearly all electrical circuits, from the simple ones shown here to much more complex networks.