Electric Circuits

What this unit covers

The topics below follow the published Physics C: E&M course framework for Unit 4. This unit is worth 15–21% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Current, Resistance & Power12 min · 3 objectivesDefine current as dQ/dt and relate it to charge transported · Compute resistance from resistivity and geometry, and apply Ohm’s law · Calculate electrical power with P = IV and its equivalent forms
• Kirchhoff’s Rules & Multiloop Circuits14 min · 3 objectivesReduce networks with series and parallel equivalent resistance · State Kirchhoff’s junction and loop rules and the conservation law behind each · Solve a multiloop circuit with two EMFs for every branch current
• RC Circuits I: Charging & the Differential Equation14 min · 3 objectivesSet up the charging-circuit differential equation from the loop rule · Solve the ODE by separation of variables to obtain q(t) and i(t) · Interpret the time constant τ = RC and use it in calculations
• RC Circuits II: Discharge, Energy & Transients13 min · 3 objectivesDerive the exponential decay q(t) = Q₀e^(−t/RC) for a discharging capacitor · Analyze circuit behavior at t = 0 and t → ∞ using capacitor limiting cases · Track energy storage and dissipation during RC transients

Formulas in Unit 4

Every term in Unit 4

All 17 terms we publish for Electric Circuits, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Current density and drift velocity

I = nqv_dA, where n is charge carrier density. Drift velocity is remarkably slow even though the signal propagates near light speed.

Resistivity and resistance

R = ρL/A. Resistivity is a material property that generally rises with temperature in metals.

Ohm's law and its limits

V = IR holds for ohmic materials at constant temperature. A filament lamp is non-ohmic because its resistance rises as it heats.

Power dissipation

P = IV = I²R = V²/R. In series, the largest resistor dissipates most; in parallel, the smallest does.

Kirchhoff's rules

Junction rule conserves charge, loop rule conserves energy. Together they solve any circuit that series-parallel reduction cannot.

Sign conventions in the loop rule

Crossing a resistor with the current is a drop; crossing a battery from − to + is a rise. Consistency decides the answer.

Internal resistance

Terminal voltage V = ε − Ir, so a battery under heavy load delivers less than its EMF.

Ammeter and voltmeter placement

An ammeter goes in series and must have near-zero resistance; a voltmeter goes in parallel and must have near-infinite resistance.

Maximum power transfer

A source delivers maximum power to a load when load resistance equals the source's internal resistance.

Reducing a network

Combine series and parallel groups from the far end back toward the source, then work forward to find individual currents and voltages.

When reduction fails

Bridge circuits and multi-source networks have no series-parallel structure, so Kirchhoff's rules with simultaneous equations are required.

Number of independent equations

One fewer than the number of junctions, plus one per independent loop. Enough to solve for every branch current.

Brightness of bulbs

Brightness follows power dissipated. Adding a bulb in series dims all of them; adding one in parallel leaves the others unchanged but raises total current.

Short circuit

A zero-resistance path around a component carries all the current, so that component receives none and dissipates no power.

Real vs ideal battery

An ideal battery holds V constant at any current; a real one has internal resistance, so terminal voltage sags under load.

Non-ohmic devices

A device whose I-V graph is not a straight line. Resistance at any point is V/I, not the slope of the graph.

Power supplied vs dissipated

A source supplies εI; the circuit dissipates I²R in every resistance including the internal one. The two balance by energy conservation.

What examiners penalize here

• Loop-rule bookkeeping wins or loses the multiloop FRQ. Commit to this convention: pick a travel direction around each loop; a resistor traversed *with* its assumed current contributes −IR and *against* it +IR; a battery crossed from − to + contributes +ε, from + to − contributes −ε. State the junction equation explicitly — graders award a point for it even before any algebra.
• Transient shortcut worth memorizing for the exam: **t = 0** → replace each uncharged capacitor with a plain wire; **t → ∞** → replace each capacitor with an open break, then find V_C from the resistors around it. Most multiple-choice RC questions are exactly these two substitutions, no exponentials required.

Practice Physics C: E&M

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 6 units of AP Physics C: E & M

1. Unit 1 · Electric Charges, Fields, and Gauss’s Law
2. Unit 2 · Electric Potential
3. Unit 3 · Conductors, Capacitors, and Dielectrics
4. Unit 4 · Electric Circuits
5. Unit 5 · Magnetic Fields
6. Unit 6 · Electromagnetic Induction