Explain that the sum of the currents into a junction is the same as the sum of the currents out of the junction

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – Series and Parallel Circuits

4.3.2 Series and Parallel Circuits

Objective

Explain that the sum of the currents into a junction is the same as the sum of the currents out of the junction (Kirchhoff’s Current Law).

Key Concept – Kirchhoff’s Current Law (KCL)

At any electrical junction (node) the algebraic sum of currents is zero:

\$\sum I{\text{in}} = \sum I{\text{out}}\$

In words, the total current flowing towards a junction equals the total current flowing away from it. This law follows from the conservation of charge.

Why KCL Holds in Series and Parallel Circuits

  • Series connection: The same current flows through each component because there is only one path for charge to move.

  • Parallel connection: The total current supplied by the source splits into branches. At the junction where the branches diverge, the incoming current equals the sum of the branch currents; where they reconverge, the sum of the branch currents equals the outgoing current.

Illustrative Example

Consider a simple parallel circuit with a battery supplying a total current \$I{\text{total}}\$ that splits into two branches carrying currents \$I1\$ and \$I_2\$.

Suggested diagram: Battery connected to a junction that splits into two resistors (R1 and R2) and then recombines.

According to KCL:

\$I{\text{total}} = I1 + I_2\$

If \$I{\text{total}} = 6\ \text{A}\$, \$I1 = 2\ \text{A}\$, then \$I_2\$ must be \$4\ \text{A}\$.

Numerical Practice

ScenarioGiven Currents (A)FindSolution
Junction A\$I{\text{in}} = 5\$, \$I1 = 2\$, \$I_2 = ?\$\$I_2\$\$I2 = I{\text{in}} - I_1 = 5 - 2 = 3\ \text{A}\$
Junction B\$I1 = 1.5\$, \$I2 = 2.5\$, \$I_{\text{out}} = ?\$\$I_{\text{out}}\$\$I{\text{out}} = I1 + I_2 = 1.5 + 2.5 = 4.0\ \text{A}\$
Three‑branch parallel circuit\$I{\text{total}} = 9\$, \$I1 = 3\$, \$I2 = 2\$, \$I3 = ?\$\$I_3\$\$I3 = I{\text{total}} - (I1 + I2) = 9 - (3 + 2) = 4\ \text{A}\$

Applying KCL in Problem Solving

  1. Identify each junction in the circuit diagram.

  2. Assign a direction to each current (conventionally away from the positive terminal of the source).

  3. Write an equation for each junction using \$\sum I{\text{in}} = \sum I{\text{out}}\$.

  4. Combine the junction equations with Ohm’s law (\$V = IR\$) and series/parallel resistance formulas to solve for the unknown quantities.

Common Mistakes to Avoid

  • Forgetting that currents entering a junction must be added together before equating to the sum of currents leaving.

  • Mixing up the sign convention – treat currents entering as positive and leaving as negative (or vice‑versa) consistently.

  • Assuming the same current flows in all branches of a parallel circuit; only series branches share the same current.

Summary

Kirchhoff’s Current Law is a fundamental principle for analysing both series and parallel circuits. It ensures charge conservation at every node, allowing us to relate the currents in different parts of a circuit and to solve for unknown values using systematic algebraic methods.