Kirchhoff's First Law

1. Definitions (Must Know)

A. Kirchhoff’s first law (junction rule / current law)

Kirchhoff’s first law states that at any junction:

• total current entering = total current leaving

Equivalently, the algebraic sum of currents at a junction is zero:

∑ I = 0

2. Key Ideas (What Earns Marks)

• It is a statement of conservation of charge: charge does not build up at an ideal junction in steady state.
• You must choose a sign convention at the junction:
  • currents entering are positive, leaving negative (or vice versa), then apply ∑ I = 0.
• Current is the same everywhere in a series branch, but it can split between parallel branches.

3. Detailed Explanations

A. Why it is true (charge conservation)

Current is rate of flow of charge: I = Δ Q/Δ t.

At a junction in steady state, charge cannot accumulate (otherwise the junction would become increasingly charged).

So the rate charge enters must equal the rate charge leaves:

∑ Iᵢₙ = ∑ Iₒᵤₜ

B. Reading a junction diagram

For example, if I₁ and I₄ enter the junction while I₂ and I₃ leave, then:

I₁ + I₄ = I₂ + I₃

4. Common Mistakes

• Mixing up “in” and “out” currents at the same junction.
• Writing multiple junction equations that are not independent (wastes time).
• Confusing conventional current direction with electron drift direction (Kirchhoff’s laws use conventional current).

5. Exam Tips

• If the question gives you current directions, use them. If not, choose directions; a negative answer means the real direction is opposite.
• Use Kirchhoff’s first law together with:
  • Kirchhoff’s second law (loops) and
  • potential divider ideas for multi-step circuit questions.

6. Worked Examples

7. Mind Stretchers