After applying Kirchhoff's rules to a two-loop circuit, you find that one branch current has a value of −3 A. What does this mean?
AYou made an arithmetic error — currents cannot be negative in a DC circuit
BThe current in that branch flows opposite to the direction you assumed, with a magnitude of 3 A
CThat branch carries no current — negative indicates zero in circuit analysis
DYour loop equation was set up incorrectly and must be redone with a revised assumed direction
A negative current value is not an error — it is the method self-correcting. It means the actual current flows opposite to the direction you assumed, with magnitude 3 A. You assumed a direction as a label for the unknown; the algebra determined both the magnitude and the true direction. The explainer states: 'Wrong guesses give negative values — not errors, just corrections.' No re-setup is needed.
Question 2 Multiple Choice
Kirchhoff's Loop Rule states that the sum of all potential differences around any closed loop equals zero. Which fundamental principle does this directly express?
AConservation of charge — charge cannot accumulate at a wire junction in steady state
BConservation of energy — a charge carrier returning to its starting point has undergone zero net energy change
COhm's law — voltage and current are proportional in all resistive elements
DNewton's third law — every voltage rise must be paired with an equal and opposite voltage drop
The Junction Rule expresses charge conservation; the Loop Rule expresses energy conservation. The explainer makes this explicit: a charge traveling around a closed loop and returning to its starting point undergoes zero net change in potential energy — just like a hiker returning to starting elevation does zero net gravitational work. Each resistor drops potential (−IR), each EMF source raises or lowers it, and the sum around any closed path must be zero by energy conservation.
Question 3 True / False
Kirchhoff's Junction Rule — the sum of currents at a node equals zero — is a direct statement of conservation of charge in steady state.
TTrue
FFalse
Answer: True
In steady state, charge neither accumulates nor disappears at a wire junction. Every coulomb flowing in must flow out — this is exactly what charge conservation requires. The Junction Rule is not an arbitrary convention; it is a consequence of the fundamental principle that charge is conserved. The explainer calls it 'charge conservation in disguise.'
Question 4 True / False
When applying the Loop Rule, traversing a resistor in the direction opposite to the assumed current gives a voltage contribution of −IR.
TTrue
FFalse
Answer: False
The sign convention is the reverse: traversing a resistor opposite to the assumed current direction gives +IR (a voltage rise), not −IR. Going through a resistor in the same direction as assumed current gives −IR (a drop, consistent with energy dissipation). Getting this sign convention backwards is one of the most common sources of errors when setting up Kirchhoff loop equations.
Question 5 Short Answer
Why is it valid to assume any direction for branch currents when setting up Kirchhoff's equations, even if your guess turns out to be wrong?
Think about your answer, then reveal below.
Model answer: Because the sign of the result carries the directional information. An assumed direction is just a label for the unknown — you're telling the algebra which direction to call 'positive.' If you get a positive value, current flows in the assumed direction; if negative, it flows opposite. The system of linear equations enforces self-consistency: wrong assumptions produce negative answers, not wrong answers. The method is self-correcting because direction information is encoded in the sign.
This is the elegant feature of the Kirchhoff method: you don't need to know the correct direction before solving, which would require knowing the answer in advance. The algebra determines both magnitude and direction simultaneously. All that matters is that you apply the sign convention consistently throughout each equation.