What are Kirchhoff's laws in the context of D.C. Circuits?

Kirchhoff's laws, fundamental to the study of D.C. Circuits in Physics, consist of two rules: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the total current entering a junction equals the total current leaving the junction. KVL asserts that the sum of the electromotive forces and potential differences around any closed loop in a circuit is zero. These laws are essential for analyzing complex circuits, a key topic in the Cambridge International A Levels curriculum.

How do you apply Kirchhoff's Current Law (KCL) in circuit analysis?

To apply Kirchhoff's Current Law (KCL) in circuit analysis, identify a junction in the circuit where multiple conductors meet. According to KCL, the sum of currents flowing into the junction must equal the sum of currents flowing out. This principle helps in setting up equations to solve for unknown currents in complex D.C. Circuits, a skill crucial for students studying Physics at the Cambridge International A Levels.

Can you explain Kirchhoff's Voltage Law (KVL) with an example?

Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop in a circuit must equal zero. For example, in a simple loop with a battery and two resistors, the voltage provided by the battery is equal to the sum of the voltage drops across the resistors. This law is used to write equations that help determine unknown voltages or resistances in D.C. Circuits, a fundamental concept in the Cambridge International A Levels Physics syllabus.

Why are Kirchhoff's laws important for solving complex D.C. Circuits?

Kirchhoff's laws are crucial for solving complex D.C. Circuits because they provide a systematic method for analyzing the flow of current and distribution of voltage in a circuit. By applying Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL), students can set up equations that allow them to solve for unknown quantities such as current, voltage, and resistance. Mastery of these laws is essential for success in the Cambridge International A Levels Physics examinations.

What are common mistakes to avoid when using Kirchhoff's laws?

Common mistakes when using Kirchhoff's laws include incorrectly identifying the direction of currents, not accounting for all voltage sources in a loop, and misapplying the signs of voltage drops and rises. It's important to consistently follow the sign conventions and carefully set up equations based on the correct application of Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). Avoiding these errors is crucial for accurately analyzing D.C. Circuits, a key component of the Cambridge International A Levels Physics curriculum.

Why is "Treating parallel resistance as direct sum" a common mistake in Kirchhoff's laws?

Why it happens: Habit from series. How to avoid it: PARALLEL: add RECIPROCALS. Two equal R in parallel: R/2. Two different: R_1 R_2/(R_1 + R_2). Source: 9702 Examiner Reports 2022-2024

D.C. CircuitsCambridge International A Levels Physics (9702)

Kirchhoff's laws

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Kirchhoff's Laws Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

KCL and KVL. Series and parallel resistor combinations.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

10.2.1 — State Kirchhoff's laws.
10.2.2 — Combine resistors series/parallel.
10.2.3 — Analyse complex circuits.

Kirchhoff's two laws

Conservation of charge + energy.

1st law (current). At any junction: sum of currents IN = sum OUT. Conservation of charge.

2nd law (voltage). Around any closed loop: sum of EMFs = sum of PDs. Conservation of energy.

Cambridge tip. Both laws stem from conservation — useful exam framing.

KCL: $\sum I$ = 0 at junction.
KVL: $\sum V$ = 0 around loop.
Conservation principles.

See the full worked example for kirchhoff's laws →

Series and parallel

Combining resistors.

Series.

Same current through each.
Voltages add.
$R_s = R_1 + R_2 + \ldots$

Parallel.

Same voltage across each.
Currents add.
$1/R_p = 1/R_1 + 1/R_2 + \ldots$

Two resistors in parallel. $R_p = R_1 R_2/(R_1 + R_2)$ .

Two equal $R$ in parallel. $R/2$ .

Mixed. Identify which parts are in series and which in parallel. Combine step by step.

Example. 6 Ω and 3 Ω parallel, then 4 Ω series:

Parallel: $1/R_p = 1/6 + 1/3 = 1/2 \Rightarrow R_p = 2$ Ω.
Total: $2 + 4 = 6$ Ω.

Cambridge tip. Sketch the circuit and label currents/voltages clearly.

Series: add.
Parallel: add reciprocals.
Step-by-step for mixed.

See the full worked example for kirchhoff's laws →

Applying KVL

Loop equations.

Method.

Choose loop direction.
Add EMFs (with sign based on direction).
Subtract PDs ( $IR$ drops) in direction of current.
Set sum to zero.

Example. EMF 12 V in series with 4 Ω and 6 Ω:

KVL: $12 = 4I + 6I = 10I \Rightarrow I = 1.2$ A.
PD across 4 Ω: 4.8 V; across 6 Ω: 7.2 V.

Cambridge tip. Show direction convention explicitly.

Loop direction.
EMFs in, PDs out.
Solve simultaneously if multiple loops.

See the full worked example for kirchhoff's laws →

How it’s examined

Kirchhoff's laws on every Paper. Most-tested: combining resistors (7-10 marks), KVL with internal resistance (8 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Kirchhoff's laws, ready to print or save as PDF.

Step-by-step worked examples — Kirchhoff's laws

Step-by-step solutions to past-paper-style questions on kirchhoff's laws, written exactly the way a tutor would explain them at the board.

1Series + parallel (7 marks)
Extended• Adapted from 9702/22 May/Jun 2024• resistors
Question
Two resistors 6.0 Ω and 3.0 Ω in parallel, in series with 4.0 Ω. Find total resistance. (7 marks)
Step-by-step solution
1. Step 1
  Parallel combination. $1/R_p = 1/6 + 1/3 = 1/2 \Rightarrow R_p = 2.0$ Ω.
2. Step 2
  Add in series.
  $R_{\text{total}} = 2.0 + 4.0 = 6.0 \text{ }\Omega$
Answer
$R = 6.0$ Ω.
2Kirchhoff's voltage law (7 marks)
Extended• KVL
Question
Battery EMF 12 V drives current through a 4 Ω and a 6 Ω resistor in series. Find current and PD across each. (7 marks)
Step-by-step solution
1. Step 1
  KVL. Sum of PDs = EMF.
  $12 = 4I + 6I = 10I \Rightarrow I = 1.2 \text{ A}$
2. Step 2
  PDs.
  $V_1 = 4 \times 1.2 = 4.8 \text{ V}, \quad V_2 = 6 \times 1.2 = 7.2 \text{ V}$
Answer
$I = 1.2$ A. $V_1 = 4.8$ V, $V_2 = 7.2$ V.
3Kirchhoff's current law (5 marks)
Extended• KCL
Question
Three currents meet at a junction: 2.0 A in, 0.8 A out one branch. Find the current in the third branch. (5 marks)
Step-by-step solution
1. Step 1
  KCL. $\sum I_{\text{in}} = \sum I_{\text{out}}$ .
2. Step 2
  Solve. $2.0 = 0.8 + I_3 \Rightarrow I_3 = 1.2$ A (out).
Answer
$I_3 = 1.2$ A out.

Key Formulae — Kirchhoff's laws

The formulae you need to memorise for kirchhoff's laws on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Kirchhoff's current law (KCL)
$\sum I_{\text{in}} = \sum I_{\text{out}}$
When to use
At any junction in a circuit. Conservation of charge.
Kirchhoff's voltage law (KVL)
$\sum E = \sum IR \quad (\text{around any loop})$
When to use
Around any closed loop. Conservation of energy.
Series resistors
$R_s = R_1 + R_2 + \ldots$
When to use
Same current, voltages add.
Parallel resistors
$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \ldots$
When to use
Same voltage, currents add.

Key Definitions and Keywords — Kirchhoff's laws

Definitions to memorise and the exact keywords mark schemes credit for kirchhoff's laws answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Kirchhoff's 1st law (current)
Examiner keyword
Sum of currents into junction = sum out. Reflects conservation of charge.
Kirchhoff's 2nd law (voltage)
Examiner keyword
Around any closed loop, sum of EMFs = sum of PDs. Reflects conservation of energy.

Common Mistakes and Misconceptions — Kirchhoff's laws

The traps other students keep falling into on kirchhoff's laws questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating parallel resistance as direct sum
9702 Examiner Reports 2022-2024
Why it happens
Habit from series.
How to avoid it
PARALLEL: add RECIPROCALS. Two equal $R$ in parallel: $R/2$ . Two different: $R_1 R_2/(R_1 + R_2)$ .

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Kirchhoff's laws — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

D.C. CircuitsCambridge International A Levels Physics (9702)

Kirchhoff's laws

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

Previous Next

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Kirchhoff's laws, ready to print or save offline.

Kirchhoff's Laws Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

KCL and KVL. Series and parallel resistor combinations.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

10.2.1 — State Kirchhoff's laws.
10.2.2 — Combine resistors series/parallel.
10.2.3 — Analyse complex circuits.

Kirchhoff's two laws

Conservation of charge + energy.

1st law (current). At any junction: sum of currents IN = sum OUT. Conservation of charge.

2nd law (voltage). Around any closed loop: sum of EMFs = sum of PDs. Conservation of energy.

Cambridge tip. Both laws stem from conservation — useful exam framing.

KCL: $\sum I$ = 0 at junction.
KVL: $\sum V$ = 0 around loop.
Conservation principles.

See the full worked example for kirchhoff's laws →

Series and parallel

Combining resistors.

Series.

Same current through each.
Voltages add.
$R_s = R_1 + R_2 + \ldots$

Parallel.

Same voltage across each.
Currents add.
$1/R_p = 1/R_1 + 1/R_2 + \ldots$

Two resistors in parallel. $R_p = R_1 R_2/(R_1 + R_2)$ .

Two equal $R$ in parallel. $R/2$ .

Mixed. Identify which parts are in series and which in parallel. Combine step by step.

Example. 6 Ω and 3 Ω parallel, then 4 Ω series:

Parallel: $1/R_p = 1/6 + 1/3 = 1/2 \Rightarrow R_p = 2$ Ω.
Total: $2 + 4 = 6$ Ω.

Cambridge tip. Sketch the circuit and label currents/voltages clearly.

Series: add.
Parallel: add reciprocals.
Step-by-step for mixed.

See the full worked example for kirchhoff's laws →

Applying KVL

Loop equations.

Method.

Choose loop direction.
Add EMFs (with sign based on direction).
Subtract PDs ( $IR$ drops) in direction of current.
Set sum to zero.

Example. EMF 12 V in series with 4 Ω and 6 Ω:

KVL: $12 = 4I + 6I = 10I \Rightarrow I = 1.2$ A.
PD across 4 Ω: 4.8 V; across 6 Ω: 7.2 V.

Cambridge tip. Show direction convention explicitly.

Loop direction.
EMFs in, PDs out.
Solve simultaneously if multiple loops.

See the full worked example for kirchhoff's laws →

How it’s examined

Kirchhoff's laws on every Paper. Most-tested: combining resistors (7-10 marks), KVL with internal resistance (8 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Kirchhoff's laws, ready to print or save as PDF.

Step-by-step worked examples — Kirchhoff's laws

Step-by-step solutions to past-paper-style questions on kirchhoff's laws, written exactly the way a tutor would explain them at the board.

1Series + parallel (7 marks)
Extended• Adapted from 9702/22 May/Jun 2024• resistors
Question
Two resistors 6.0 Ω and 3.0 Ω in parallel, in series with 4.0 Ω. Find total resistance. (7 marks)
Step-by-step solution
1. Step 1
  Parallel combination. $1/R_p = 1/6 + 1/3 = 1/2 \Rightarrow R_p = 2.0$ Ω.
2. Step 2
  Add in series.
  $R_{\text{total}} = 2.0 + 4.0 = 6.0 \text{ }\Omega$
Answer
$R = 6.0$ Ω.
2Kirchhoff's voltage law (7 marks)
Extended• KVL
Question
Battery EMF 12 V drives current through a 4 Ω and a 6 Ω resistor in series. Find current and PD across each. (7 marks)
Step-by-step solution
1. Step 1
  KVL. Sum of PDs = EMF.
  $12 = 4I + 6I = 10I \Rightarrow I = 1.2 \text{ A}$
2. Step 2
  PDs.
  $V_1 = 4 \times 1.2 = 4.8 \text{ V}, \quad V_2 = 6 \times 1.2 = 7.2 \text{ V}$
Answer
$I = 1.2$ A. $V_1 = 4.8$ V, $V_2 = 7.2$ V.
3Kirchhoff's current law (5 marks)
Extended• KCL
Question
Three currents meet at a junction: 2.0 A in, 0.8 A out one branch. Find the current in the third branch. (5 marks)
Step-by-step solution
1. Step 1
  KCL. $\sum I_{\text{in}} = \sum I_{\text{out}}$ .
2. Step 2
  Solve. $2.0 = 0.8 + I_3 \Rightarrow I_3 = 1.2$ A (out).
Answer
$I_3 = 1.2$ A out.

Key Formulae — Kirchhoff's laws

The formulae you need to memorise for kirchhoff's laws on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Kirchhoff's current law (KCL)
$\sum I_{\text{in}} = \sum I_{\text{out}}$
When to use
At any junction in a circuit. Conservation of charge.
Kirchhoff's voltage law (KVL)
$\sum E = \sum IR \quad (\text{around any loop})$
When to use
Around any closed loop. Conservation of energy.
Series resistors
$R_s = R_1 + R_2 + \ldots$
When to use
Same current, voltages add.
Parallel resistors
$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \ldots$
When to use
Same voltage, currents add.

Key Definitions and Keywords — Kirchhoff's laws

Definitions to memorise and the exact keywords mark schemes credit for kirchhoff's laws answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Kirchhoff's 1st law (current)
Examiner keyword
Sum of currents into junction = sum out. Reflects conservation of charge.
Kirchhoff's 2nd law (voltage)
Examiner keyword
Around any closed loop, sum of EMFs = sum of PDs. Reflects conservation of energy.

Common Mistakes and Misconceptions — Kirchhoff's laws

The traps other students keep falling into on kirchhoff's laws questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating parallel resistance as direct sum
9702 Examiner Reports 2022-2024
Why it happens
Habit from series.
How to avoid it
PARALLEL: add RECIPROCALS. Two equal $R$ in parallel: $R/2$ . Two different: $R_1 R_2/(R_1 + R_2)$ .

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Kirchhoff's laws — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Kirchhoff's laws

Short Study Notes in the form of Slides

Detailed Notes

What you’ll learn

How it’s examined

1Series + parallel (7 marks)

2Kirchhoff's voltage law (7 marks)

3Kirchhoff's current law (5 marks)

Kirchhoff's current law (KCL)

Kirchhoff's voltage law (KVL)

Series resistors

Parallel resistors

Kirchhoff's 1st law (current)

Kirchhoff's 2nd law (voltage)

✕Treating parallel resistance as direct sum

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Kirchhoff's laws — frequently asked questions

Kirchhoff's laws

Short Study Notes in the form of Slides

Detailed Notes

What you’ll learn

How it’s examined

1Series + parallel (7 marks)

2Kirchhoff's voltage law (7 marks)

3Kirchhoff's current law (5 marks)

Kirchhoff's current law (KCL)

Kirchhoff's voltage law (KVL)

Series resistors

Parallel resistors

Kirchhoff's 1st law (current)

Kirchhoff's 2nd law (voltage)

✕Treating parallel resistance as direct sum

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Kirchhoff's laws — frequently asked questions