Skip to content
Know.itKnow.it
Create an animated lesson
On request

Read the answer free. Creating a lesson uses your daily or stored credits; review the language and settings before starting.

What are Kirchhoff's laws?

Class 12 PhysicsNCERT chapter: Current Electricityइसे हिंदी में पढ़ें

Exam-ready answer

Kirchhoff's two rules are used to analyse electric circuits. Junction rule: at any junction, the sum of currents entering equals the sum of currents leaving (ΣI = 0), which follows from conservation of charge. Loop rule: the algebraic sum of changes in potential around any closed loop is zero (ΣΔV = 0), which follows from conservation of energy.

Explanation

Junction rule: charge cannot pile up at a junction in a steady circuit, so whatever current flows into a junction must flow out. If currents of 3 A and 2 A enter a junction and only one wire leaves it, that wire carries 5 A. Taking currents entering as positive and currents leaving as negative, their algebraic sum at every junction is zero.

Loop rule: electric potential has a single value at each point of a circuit. Starting at a point, going round a closed loop and coming back, the total rise and fall in potential must add up to zero. Sign convention: crossing a resistor in the direction of current gives a drop of −IR; crossing a cell from its negative to its positive terminal gives a rise of +ε.

To solve a circuit, assign a current with an assumed direction to each branch, apply the junction rule at the junctions, and write loop equations for independent loops. Then solve the equations together. If a current comes out negative, it simply flows opposite to the assumed direction. The balance condition of the Wheatstone bridge is also derived using these two rules.

Points to remember

  1. Junction rule (first rule): sum of currents entering a junction = sum of currents leaving it.
  2. The junction rule is based on conservation of charge.
  3. Loop rule (second rule): the algebraic sum of changes in potential around any closed loop is zero.
  4. The loop rule is based on conservation of energy, since the electrostatic force is conservative.
  5. Signs: −IR across a resistor taken along the current; +ε across a cell taken from − to + terminal.

Exam tip

Draw the circuit, mark each current with an arrow, and state the sign convention before writing loop equations. Name the conservation law behind each rule: charge for the junction rule, energy for the loop rule.

Questions students also ask

Why is the junction rule based on conservation of charge?
In steady state, charge does not accumulate at any point in a circuit. So the charge flowing into a junction each second must equal the charge flowing out each second. Since current is charge per second, the currents in equal the currents out.
Is the loop rule valid for any closed path?
Yes. Potential has a unique value at every point, so after going around any closed loop and returning to the start, the net change in potential is zero. The rule applies to every closed loop in a circuit, whether or not the loop contains a cell.
What if the assumed direction of a current is wrong?
The equations still work. Solving them gives a negative value for that current, which only means the actual current flows opposite to the assumed direction. The magnitude obtained is correct, so there is no need to redo the problem.

Chapter labels help you find the topic in your textbook. Check your own edition: chapter names and order can change. These are Know.it explanations, not official NCERT solutions.