(b) Kirchhoff’s first and second laws applied to electrical circuits

The idea

Kirchhoff’s first law states that the sum of currents entering a junction equals the sum leaving it, because charge is conserved. At a junction where 2.0 A enters and splits into I₁ and I₂, I₁ + I₂ = 2.0 A. Kirchhoff’s second law states that around any closed loop, the sum of e.m.f.s equals the sum of p.d.s, because energy is conserved per unit charge. In a series circuit with a 6.0 V battery and two resistors, the p.d.s add to 6.0 V. These laws apply to any circuit, including series and parallel combinations, and are used to analyse unknown currents and voltages. They are fundamental to circuit analysis and are assessed in multiple-choice questions requiring calculation or identification of correct statements.

What earns the marks

• Kirchhoff’s first law: sum of currents entering a junction equals sum leaving, based on conservation of charge.
• Kirchhoff’s second law: around any closed loop, sum of e.m.f.s equals sum of p.d.s, based on conservation of energy.
• Application to junctions: at a node, total current in equals total current out, e.g. I₁ = I₂ + I₃.
• Application to loops: in a series circuit, the sum of potential differences across components equals the supply e.m.f.
• Use in circuit analysis: these laws allow calculation of unknown currents and voltages in series and parallel networks.

Common mistakes and how to put them right

• Misunderstanding: Kirchhoff’s first law applies to any point in a circuit, not just junctions.

  Put it right: It applies specifically to junctions where current can split or combine.

• Misunderstanding: Kirchhoff’s second law applies only to simple series circuits.

  Put it right: It applies to any closed loop, including those with parallel branches.

• Misunderstanding: Kirchhoff’s laws are independent of conservation principles.

  Put it right: They are direct consequences of conservation of charge and energy.

• Misunderstanding: The sum of currents entering a junction is always zero.

  Put it right: The algebraic sum is zero if directions are considered, but the sum of magnitudes entering equals that leaving.

Exam tips

• For multiple-choice questions, check each option against the laws: first law involves currents at a junction, second law involves voltages around a loop.
• When calculating, ensure you use consistent signs for currents and voltages; define a direction and stick to it.
• Remember that in a series circuit, current is the same everywhere, so Kirchhoff’s first law is trivially satisfied at any point.