Kirchhoff's Junction and Loop Rules

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

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.

Writing +ε + IR = 0 for a resistor traversed in the current direction is wrong because moving along current through a resistor is a potential drop, not a rise.

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.

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. 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. 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.

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. 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. At a junction, current I₁ enters and splits into 2 A and 3 A, so I₁ = 5 A. For a single loop with ε = 12 V, R1 = 2 ohm and R2 = 4 ohm in series, choose clockwise current I. Loop equation: +12 - 2I - 4I = 0, so 6I = 12 and I = 2 A. The resistor drops are 4 V and 8 V, adding to 12 V. 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. Writing +ε + IR = 0 for a resistor traversed in the current direction is wrong because moving along current through a resistor is a potential drop, not a rise.