Apply Kirchhoff’s laws to junctions and loops
Use charge conservation at junctions and energy conservation around complete circuit loops.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 10. These original circuit diagrams and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use current, potential difference, resistance, energy and charge with consistent circuit directions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What physical conservation principle underlies Kirchhoff’s first law?
What you will learn
- Recall Kirchhoff's first law and relate it to conservation of charge
- Recall Kirchhoff's second law and relate it to conservation of energy
- Use signed current and potential changes to solve simple circuits
The junction law is conservation of charge
Kirchhoff's first law states that the total current entering a junction equals the total current leaving it. This is a consequence of conservation of charge: charge cannot build up indefinitely at an ideal circuit junction, so the rate of charge flow in balances the rate flowing out.
Choose a direction for each branch current. If a solved current is negative, the actual direction is opposite to the chosen arrow. This sign convention lets one equation handle unknown branch directions consistently.
The loop law is conservation of energy
Kirchhoff's second law states that the algebraic sum of potential changes around a complete closed loop is zero. This is a consequence of conservation of energy: energy supplied per charge by sources balances energy transferred per charge by components around that loop.
Choose a loop direction and record source rises and component drops with consistent signs. A component drop is V = IR for an ohmic resistor. The sum of rises equals the sum of drops for the selected loop.
Pause and explain
What should the signed potential changes around a closed loop sum to?
Worked example
At a junction, 2.0 A enters and 0.70 A and I leave. Find I. In a loop with a 12 V source and 4.0 V and V drops, find V.
Show the worked solution
- Junction: 2.0 = 0.70 + I, so I = 1.3 A.
- Loop: 12 − 4.0 − V = 0.
- Thus V = 8.0 V.
Answer I = 1.3 A; V = 8.0 V.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
At a junction, 1.8 A enters. Two outgoing branch currents are 0.45 A and I. Find I.
Give me a hint
Set total entering current equal to total leaving current.
Compare my reasoning
- 1.8 = 0.45 + I.
- I = 1.8 − 0.45.
- State the branch direction as leaving, as drawn.
I = 1.35 A leaving the junction.
Look for these in your work
- Junction equation written
- Unknown isolated
- Direction interpreted
A 9.0 V source drives a series loop with drops of 2.5 V and V. Find V using Kirchhoff’s second law.
Give me a hint
The signed rise and drops around the loop sum to zero.
Compare my reasoning
- 9.0 − 2.5 − V = 0.
- V = 9.0 − 2.5.
- Check the drops total the source rise.
V = 6.5 V.
Look for these in your work
- Loop signs consistent
- Unknown p.d. found
- Energy balance checked
At a junction 0.60 A enters; two currents labelled leaving are 0.90 A and I. Find I and explain its sign.
Give me a hint
Use the directions shown in the signed junction equation.
Compare my reasoning
- Write 0.60 = 0.90 + I.
- I = −0.30 A.
- The negative sign means actual current is 0.30 A entering, opposite the drawn leaving arrow.
I = −0.30 A relative to the chosen arrow; actual current is 0.30 A into the junction.
Look for these in your work
- Signed equation correct
- Negative value retained
- Physical direction explained
Common mistakes
- Adding currents without distinguishing entering from leaving
- Mixing potential rises and drops with inconsistent signs
- Interpreting a negative solved current as impossible instead of reversed direction
What can you explain now?
What physical conservation principle underlies Kirchhoff’s first law?
Compare with the explanation
Conservation of charge
Current entering balances current leaving at a junction.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do the two Kirchhoff laws express separate conservation ideas?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.