Question

Explain Kirchhoff's laws related to electrical circuits.

Hint:

Junction law: sum of currents at a node is zero (charge conservation). Loop law: sum of EMFs equals sum of IR drops around a closed loop (energy conservation).

Answer 1

Kirchhoff gave two laws that let us analyse any electrical network, even ones that cannot be reduced by simple series and parallel rules.

Step 1: Kirchhoff's Junction Law (Current Law, KCL).
At any junction (node) in an electrical circuit, the algebraic sum of currents is zero. In other words, the total current flowing into a junction equals the total current flowing out of it.
\[ \sum I = 0 \quad\Rightarrow\quad \sum I_{in} = \sum I_{out} \]
Taking currents entering the junction as positive and those leaving as negative, their sum is zero.

Step 2: Conservation principle behind KCL.
This law is a statement of conservation of electric charge. Charge cannot accumulate at a junction (it is a point), so whatever charge enters per second must leave per second. Hence the net current at the node is zero.

Step 3: Kirchhoff's Loop Law (Voltage Law, KVL).
In any closed loop (mesh) of a circuit, the algebraic sum of all potential differences (EMFs and IR drops) is zero.
\[ \sum \Delta V = 0 \quad\Rightarrow\quad \sum \varepsilon = \sum I R \]
Sign convention: while traversing the loop, a potential rise is taken positive and a drop negative; the EMF of a cell is positive if we go from its negative to positive terminal, and an IR term is negative when we move along the direction of current.

Step 4: Conservation principle behind KVL.
This law is a statement of conservation of energy. When a unit charge is carried once around a closed loop and returns to the starting point, the net change in its potential energy is zero, so the algebraic sum of all potential changes around the loop is zero.

Step 5: Summary.
The junction law fixes the currents (based on charge conservation) and the loop law fixes the potential differences (based on energy conservation). Applied together they give enough independent equations to solve for every unknown current in a network.
\[\boxed{\text{KCL: } \sum I = 0 \ (\text{charge}), \quad \text{KVL: } \sum \varepsilon = \sum IR \ (\text{energy})}\]