A node in a circuit has three branches: currents I₁ and I₂ flow in, and I₃ flows out. What does KCL tell you about these currents?
AI₁ + I₂ = I₃
BI₁ - I₂ + I₃ = 0
CI₁ × I₂ = I₃
DI₁ + I₂ + I₃ = 0, regardless of direction
KCL states that the sum of currents entering a node equals the sum of currents leaving it. With I₁ and I₂ entering and I₃ leaving, conservation of charge requires I₁ + I₂ = I₃. Option D would be correct if all currents were defined with the same sign convention (all into or all out of the node), in which case the algebraic sum is zero — but mixing actual directions gives I₁ + I₂ = I₃.
Question 2 Multiple Choice
A loop contains a 12 V source and three resistors with voltage drops of 3 V, 5 V, and 4 V. You apply KVL around this loop. Which statement is correct?
A12 − 3 − 5 − 4 = 0 confirms energy conservation — this is a valid KVL equation
BThe sum of drops exceeds the source voltage, so KVL is violated in this circuit
CThe drops must sum to more than 12 V to account for energy losses in the resistors
DKVL only applies if all resistors are in series; it cannot be applied to a general loop
KVL states that the sum of all voltage rises and drops around any closed loop is zero. The 12 V source is a rise (+12), and the resistor drops are −3, −5, −4 V. Sum: 12 − 3 − 5 − 4 = 0. This is exactly energy conservation: a charge that travels around the loop returns to its starting potential, gaining and losing exactly equal amounts of energy.
Question 3 True / False
KCL implies that current is partially 'used up' or consumed by a resistor, so the current leaving a resistor is typically less than the current entering it.
TTrue
FFalse
Answer: False
This is the most common misconception about current and KCL. Resistors convert electrical energy into heat, but they do not consume charge. The same current that enters a resistor exits the other side — KCL guarantees it. What changes across a resistor is voltage (potential energy per charge), not current (charge flow rate). 'Voltage drops' across resistors; current is conserved.
Question 4 True / False
KCL and KVL together provide exactly enough independent equations to solve for all unknown branch currents and voltages in any circuit.
TTrue
FFalse
Answer: True
For a circuit with N nodes and B branches, KCL yields N−1 independent node equations and KVL yields B−N+1 independent loop equations. These two counts add to exactly B — one equation per unknown branch quantity. This completeness is guaranteed by the topology of the circuit graph, which is why the two laws together form a complete and solvable system for any circuit.
Question 5 Short Answer
Why do physicists say KVL is a consequence of energy conservation and KCL is a consequence of charge conservation?
Think about your answer, then reveal below.
Model answer: KCL follows from the fact that electric charge cannot accumulate at a node in steady state — every electron that flows in must flow out. If charge built up, an ever-growing electric field would quickly stop current flow. KVL follows from energy conservation: a charge carrier traveling around a closed loop and returning to its starting point must gain and lose exactly equal amounts of energy, so the net potential change around any loop is zero. If it were not, charges could spontaneously gain energy on each loop — violating conservation.
Connecting the circuit laws to their physical foundations helps you know when they apply and why: KCL holds as long as charge isn't accumulating (valid for DC and quasi-static AC), and KVL holds as long as changing magnetic flux through loops is negligible (valid for lumped-circuit models). Knowing the foundations lets you recognize the edge cases.