Build and measure DC circuits with a virtual breadboard
Kirchhoff's laws govern DC circuit analysis. KVL states that the sum of voltage drops around any closed loop equals zero (energy conservation). KCL states that the sum of currents at any node equals zero (charge conservation). Together they allow systematic solution of any DC circuit. Ohm's Law (V=IR) connects voltage, current, and resistance at each element.
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Sign in →Most physics labs end where real engineering starts: at the breadboard. Drop a battery, three resistors, and a multimeter on a virtual board, run wires between rows, and you can build any DC network you can sketch. Probe a node with the red lead and the multimeter shows you a voltage; clip it inline and it shows you a current. Behind every reading sit two conservation laws — Kirchhoff's voltage rule (energy gained around a loop equals energy lost) and Kirchhoff's current rule (charge in equals charge out at every node) — combined with V = IR at each component. AP Physics 2 expects students not just to memorize the formulas but to take real measurements, compare them to predictions, and explain mismatches. In the lab below, build a circuit, predict the meter reading, then probe it and see how close you got.
MisconceptionAn ammeter has to go in parallel with the resistor I'm measuring, like a voltmeter does.
CorrectAmmeters go in series, voltmeters go in parallel. An ammeter measures the current through a path, so it has to be inserted into that path; a voltmeter measures the voltage across two points, so it bridges them. Wiring an ammeter in parallel can create a near-short path and change the circuit you meant to measure.
MisconceptionKirchhoff's voltage rule says voltage gets used up around the loop until it runs out at the end.
CorrectKVL says energy per charge gained from the source equals energy per charge dropped across circuit elements in the loop — the signed changes sum to zero. Voltage is not a substance that disappears; it is a difference in electric potential energy per charge between two points.
MisconceptionThe current splits evenly between two paths no matter what the resistor values are.
CorrectBranches share voltage, not necessarily current. If two branches have the same voltage across them, their currents are set by I = V/R. Equal currents require equal resistance. Otherwise, the lower-resistance path carries more current.
MisconceptionA capacitor in a DC circuit blocks everything, so it never matters.
CorrectA capacitor changes a DC circuit during charging and discharging. Right after connection, current can flow while charge builds on the plates; later, the current decreases as the capacitor voltage approaches the source voltage. The resistance and capacitance together set the time scale.
Three usual suspects: ammeters have a small but nonzero resistance, voltmeters have a large but finite resistance and pull a tiny current, and real wires are not perfect conductors. AP Physics 2 mostly idealizes these away, but you should expect about 1–2% error even in good simulations and noticeably more with real benchtop gear.
Pick a direction around each loop, label voltage rises through the source from − to + as positive and drops across resistive elements in the direction of current as negative, and write the sum equal to zero for each loop. Combine those loop equations with Kirchhoff's current rule at shared nodes. In this lab, the Voltage Divider and basic series/parallel measurements are good places to compare loop reasoning with direct meter readings.
Ohm's Law is local — it relates V, I, and R at a single ohmic component. Kirchhoff's laws are global — they enforce energy and charge conservation across the whole network. To solve a circuit you often need both: KVL and KCL set up relationships around loops and at nodes, while V = IR fills in each resistor's voltage-current relationship.
CHA-2.A asks students to model current and resistance in DC circuits, applying Ohm's Law (V = IR) at every component while using Kirchhoff's voltage and current laws to constrain the network. The virtual breadboard is the simulation analog of the lab AP graders expect students to have done — wiring components, choosing measurement points, and explaining how readings confirm V = IR alongside KVL and KCL. Free-response questions on circuits routinely ask exactly this measurement-and-explanation pattern.
A capacitor stores charge, so its voltage changes as charge accumulates on its plates. The circuit current is largest at the start of charging and then decreases as the capacitor voltage approaches the source voltage. The time constant τ = RC sets the pace: increasing resistance or capacitance makes the charging process take longer.