Kirchhoff’s Laws Solved: How to Crack Any Circuit in 4 Steps
Junction and loop rules for CBSE and JEE circuit numericals.
Multi-Loop DC Circuit
Key relation
ΣI_in = ΣI_out, ΣΔV_loop = 0
Branch Currents
Kirchhoff Laws
Kirchhoff’s junction rule (KCL) states algebraic sum of currents at a node is zero: charge cannot accumulate at a junction in steady DC circuits. Currents entering are opposite sign to currents leaving—pick one sign convention and stick to it.
The loop rule (KVL) states sum of potential changes around any closed loop is zero. Energy gained from sources equals energy lost across resistors and other elements. Traversing a resistor with current: voltage drop is IR in direction of current.
KCL and KVL
Exam tip
Sign errors dominate. When walking a loop, rising through a battery from − to + adds +ε; falling through resistor in direction of current subtracts IR. Opposite traversal flips signs—write the walk direction beside each term.
Four-step method: redraw clearly; assign currents; write KCL at (n−1) junctions; write KVL for enough independent loops to solve unknowns. Number of unknown currents equals number of independent equations.
Study strategy
Wheatstone bridge balance condition P/Q = R/S when galvanometer reads zero—no current in middle branch. Unbalanced bridge needs full Kirchhoff treatment or delta-Y transformation.
Try interactive calculators
Frequently Asked Questions
How many loops do I need?
Use enough independent loops to get one equation per unknown current. Typically (# branches − # junctions + 1) equations.