1. Why Kirchhoff’s Laws Are Needed
Ohm’s law works well for simple circuits. But when circuits have multiple loops, branches or junctions, we need a more general method. This is where Kirchhoff’s current and voltage laws help. They allow us to analyse any circuit, no matter how complex.
2. Kirchhoff’s Current Law (KCL)
KCL is based on the principle of conservation of charge. It tells us how current behaves at a junction or node in a circuit.
2.1. Definition of KCL
Kirchhoff’s Current Law states that the algebraic sum of currents entering a junction is equal to the algebraic sum of currents leaving the junction.
\( \sum I_{\text{in}} = \sum I_{\text{out}} \)
2.2. Meaning of the Law
This law simply says that no charge accumulates at a junction. Whatever charge comes in must go out. If currents entering are taken as positive, and currents leaving are taken as negative, the sum is zero.
\( \sum I = 0 \)
2.2.1. Simple Example
If 3 A and 2 A currents enter a junction, and one branch carries 4 A away, the remaining branch must carry:
\( I = 3 + 2 - 4 = 1\,\text{A} \)
3. Kirchhoff’s Voltage Law (KVL)
KVL is based on the principle of conservation of energy. It tells us how voltage behaves in a loop of a circuit.
3.1. Definition of KVL
Kirchhoff’s Voltage Law states that the algebraic sum of all voltages in a closed loop is zero.
\( \sum V = 0 \)
3.2. Meaning of the Law
As a charge moves around a loop, it gains energy in sources like cells and loses energy in resistors. The net change must be zero because energy is conserved.
3.2.1. Loop Interpretation
While writing KVL, rises in potential are taken as positive and drops in potential are taken as negative.
Example: In a loop with a 10 V battery and a resistor with voltage drop 6 V:
\( +10 - 6 - 4 = 0 \)
4. Using Both Laws Together
In most multi-loop circuits, we apply KCL to junctions to find relationships between currents and apply KVL to loops to find voltage relations. Solving the resulting equations gives unknown currents and voltages.
4.1. Simple Strategy
- Apply KCL at nodes to relate currents.
- Apply KVL in loops to relate voltages.
- Solve simultaneously to find unknowns.
5. Example to Visualise KCL and KVL
Imagine water pipes meeting at a junction. The total water flowing in must equal the water flowing out—this is KCL. Now imagine walking around a complete pipe loop: the total rise and drop in water pressure must balance—this is KVL.