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Kirchhoff's Junction and Loop Rules

Kirchhoff's junction rule states that the algebraic sum of currents at a junction is zero, based on conservation of charge. Kirchhoff's loop rule states that the algebraic sum of potential changes around any closed loop is zero, based on conservation of energy.

In one line: Junction rule counts charge; loop rule counts energy.

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Understand it

  • Kirchhoff's rules extend circuit analysis beyond simple series and parallel circuits.
  • At a junction, charge cannot accumulate in steady state, so total current entering equals total current leaving.
  • Around a closed loop, a charge returns to its starting point with no net change in potential, so rises due to sources and drops across resistors balance.
  • The rules work only when signs are assigned consistently.

Example

At a junction, if currents 2 A and 3 A enter and current I leaves, then I = 5 A. In a loop with a 10 V cell and two resistors carrying 2 A through 2 ohm and 3 ohm, the drops are 4 V and 6 V, which balance the 10 V rise.

Formula and rule

Junction rule: ΣI = 0, or total current entering a junction equals total current leaving.

Loop rule: ΣV = 0 around a closed loop.

Across a resistor, moving in the direction of current gives a potential drop -IR; moving opposite to current gives +IR.

Across a cell from negative to positive terminal gives +ε; from positive to negative gives -ε.

Use for steady circuits where charge distribution is not changing with time.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

At a junction, current I1 enters and splits into 2 A and 3 A, so I1 = 5 A.

  1. 1For a single loop with ε = 12 V, R1 = 2 ohm and R2 = 4 ohm in series, choose clockwise current I.
  2. 2Loop equation: +12 - 2I - 4I = 0, so 6I = 12 and I = 2 A.
  3. 3The resistor drops are 4 V and 8 V, adding to 12 V.

Method you can reuse

  1. 1Assign current directions in all branches.
  2. 2Apply the junction rule at independent junctions.
  3. 3Choose loop directions.
  4. 4Write loop equations using the same sign convention throughout.
  5. 5Solve simultaneous equations.
  6. 6Interpret negative signs as reversed current directions.

Visual tip

A circuit diagram should mark assumed current directions in each branch, junction labels, loop directions, cell polarities, resistor values, and sign convention for potential rises and drops.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What does a negative current value mean in a Kirchhoff's rules problem?

Think first, then show answer
A negative current value means the assumed direction of that current was opposite to its actual direction. The magnitude is still useful, and the sign tells you to reverse the direction in the final interpretation.

Common wrong answer

Writing +ε + IR = 0 for a resistor traversed in the current direction.

Why it loses marks: Moving along current through a resistor is a potential drop, not a rise.

Don't mix this up

A common error is changing the sign convention halfway through the loop equation. Once a loop direction is chosen, potential rises and drops must be treated consistently.

Exam tip

If the calculated current is negative, do not panic. It means the actual current direction is opposite to the direction initially assumed.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked through multi-loop circuit equations, assertion-reason questions on conservation laws, sign convention questions, and finding unknown currents or potential differences in bridge-like networks.
  1. 1

    Enough for 1 mark

    Kirchhoff's junction rule states that the algebraic sum of currents at a junction is zero, based on conservation of charge. Kirchhoff's loop rule states that the algebraic sum of potential changes around any closed loop is zero, based on conservation of energy.

  2. 2

    Add for 2 marks

    Example: At a junction, if currents 2 A and 3 A enter and current I leaves, then I = 5 A. In a loop with a 10 V cell and two resistors carrying 2 A through 2 ohm and 3 ohm, the drops are 4 V and 6 V, which balance the 10 V rise.

  3. 3

    Add for 3 marks

    Kirchhoff's rules extend circuit analysis beyond simple series and parallel circuits.

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