PhysicsChapter 11: Electricity

Kirchhoff's Loop Rule

Kirchhoff's loop rule states that the algebraic sum of all potential changes around any closed circuit loop is zero. It follows from conservation of energy.

Key equation

∑ Δ V=0

Sign rules

Traversal	Potential change
Across a resistor with current	−IR
Across a resistor against current	+IR
Through a source from − to + terminal	+ε
Through a source from + to − terminal	−ε

Choose a loop direction; clockwise or anticlockwise both work.
Keep the chosen direction throughout the equation.
Use the current arrow to decide each resistor sign.
Use terminal polarity to decide each emf sign.
A negative solved current means the actual direction is opposite to the assumed arrow.

Quick solved example

A 12 V source is connected to 2 Ω and 4 Ω in series.

Key equation

+12-2I-4I=0

Key equation

I=122+4=2\ A

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Kirchhoff's Loop Rule

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Key Point 1

Kirchhoff's loop rule follows from conservation of energy.

Key Point 2

The algebraic sum of potential changes around a closed loop is zero.

Key Point 3

Across a resistor: −IR with current and +IR against current.

Key Point 4

Across a source: +ε from negative to positive and −ε from positive to negative.

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8 concept questions
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Explanation after each answer

Exam Practice

Statement
Q1. State Kirchhoff's loop rule and name its physical basis.
Signs
Q2. State the sign convention for resistors and sources in a loop equation.
Numerical
Q3. A 12 V source drives 2 Ω and 4 Ω in series. Use the loop rule to find current.
Reasoning
Q4. Why may either clockwise or anticlockwise traversal be chosen?
Application
Q5. How are Kirchhoff's rules used together in a multi-loop circuit?

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Traversal

Potential change

Across a resistor with current

−IR

Across a resistor against current

+IR

Through a source from − to + terminal

+ε

Through a source from + to − terminal

−ε

Exam Practice

Statement

Q1. State Kirchhoff's loop rule and name its physical basis.

Signs

Q2. State the sign convention for resistors and sources in a loop equation.

Numerical

Q3. A 12 V source drives 2 Ω and 4 Ω in series. Use the loop rule to find current.

Reasoning

Q4. Why may either clockwise or anticlockwise traversal be chosen?

Application

Q5. How are Kirchhoff's rules used together in a multi-loop circuit?

Kirchhoff's Loop Rule

Sign rules

Quick solved example

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Important points

Common mistakes

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Kirchhoff's Loop Rule

Key Point 1

Key Point 2

Key Point 3

Key Point 4

Ready to test yourself?

Exam Practice

Kirchhoff's Loop Rule

Sign rules

Quick solved example

Did you understand this topic?

Exam Focus

Important points

Common mistakes

Revision Zone

Kirchhoff's Loop Rule

Key Point 1

Key Point 2

Key Point 3

Key Point 4

Ready to test yourself?

Exam Practice