Unit 11 · Electric Circuits

Electric current ● (core concept) — I = Δq/Δt: the rate at which charge passes through a cross-sectional area of a wire. It has a direction but is not a vector; its SI unit is the ampere.

Electromotive force (emf) ● (core concept) — The electric potential difference a source (e.g., a battery) provides, driving charge motion in a circuit. It is a potential difference, not a force, and is the potential difference measured across the terminals when no current flows.

Conventional current vs. electron flow ● (core concept) — Conventional current points in the direction positive charge would move; circuit diagrams are drawn with it. In real metal circuits the moving charges are electrons, which drift opposite the conventional current. Zero current means zero net charge-carrier motion, though individual carriers still move randomly.

Closed, open, and short circuits ● (core concept) — A closed circuit is a complete loop charges can flow through. An open circuit has a break so charges cannot flow. A short circuit is a path charges can flow through with no change in potential difference (essentially zero resistance).

Circuit schematic ● (core concept) — A diagram using standard symbols (battery, resistor, bulb, capacitor, switch, ammeter A, voltmeter V) to describe a circuit's physical arrangement. A single element may belong to multiple loops, and variable elements are marked with a diagonal arrow.

Resistance ● (core concept) — A measure of how strongly an object opposes the motion of electric charge through it. For a uniform resistor, R = ρℓ/A: proportional to resistivity ρ and length ℓ, inversely proportional to cross-sectional area A.

Resistivity ● (core concept) — An intrinsic property of a material (set by its atomic and molecular structure) quantifying how strongly it opposes charge motion. A conductor's resistivity typically rises with temperature; an ohmic material's resistivity is constant.

Ohm's law ● (core concept) — I = ΔV/R: the current through a conductive element equals the potential difference across it divided by its resistance.

Ohmic material ● (core concept) — A material with constant resistance for all currents — one that obeys Ohm's law. Its resistance is the inverse of the slope of a current-versus-potential-difference graph. Resistors also convert electrical energy to thermal energy, which can warm them and change their behavior.

Electric power ● (core concept) — P = IΔV = I²R = (ΔV)²/R: the rate at which energy is transferred, converted, or dissipated by a circuit element, set by its current and the potential difference across it. A bulb's brightness increases with its power.

Series connection ● (core concept) — A connection in which any charge passing through one element must pass through every element in the connection, with no alternate path. Every element in series carries the same current.

Parallel connection ● (core concept) — A connection offering charges two or more alternate paths. The potential difference is the same across each parallel path.

Equivalent resistance: series ● (core concept) — R_eq = ΣR_i: resistors in series add directly. Adding a series resistor always increases the total resistance.

Equivalent resistance: parallel ● (core concept) — 1/R_eq = Σ(1/R_i): for resistors in parallel, the inverses add. More parallel paths always decrease the equivalent resistance below the smallest individual resistor.

Ideal battery and ideal wires ● (core concept) — An ideal battery has negligible internal resistance; ideal wires have negligible resistance and can normally be neglected when other resistive elements are present.

Internal resistance ● (core concept) — A real (nonideal) battery behaves like an ideal battery in series with a small internal resistance r. When current flows, the terminal voltage drops below the emf: V_terminal = emf − Ir.

Ammeter ● (core concept) — A meter that measures current at a specific point; it must be connected in series with the element being measured. An ideal ammeter has zero resistance so it does not change the circuit's current.

Voltmeter ● (core concept) — A meter that measures potential difference between two points; it must be connected in parallel across the element being measured. An ideal voltmeter has infinite resistance so no charge flows through it.

Direct current (DC) ● (core concept) — Current that flows in one constant direction, driven by a constant potential difference — as supplied by a battery. AP Physics 2 circuits are DC circuits.

Terminal voltage ● (core concept) — The potential difference measured across a battery's terminals while it supplies current. For a real battery, V_terminal = emf − Ir, which is less than the emf whenever current flows through the internal resistance.

Kirchhoff's loop rule ● (core concept) — The sum of the potential differences across all elements in a single closed loop equals zero (ΣΔV = 0). It is a consequence of conservation of energy: charges moving around a loop end with the same energy they started with.

Multiloop circuit ● (core concept) — A circuit with more than one closed loop, so that current can split at junctions and take alternate paths. Analyzing it requires applying Kirchhoff's loop rule to each loop and the junction rule at each junction.

Kirchhoff's junction rule ● (core concept) — At any junction, the total charge entering per unit time equals the total charge leaving per unit time (ΣI_in = ΣI_out). It is a consequence of conservation of electric charge.

Equivalent capacitance: series ● (core concept) — 1/C_eq = Σ(1/C_i): for capacitors in series the inverses add, so C_eq is smaller than the smallest individual capacitor. By conservation of charge, series capacitors all carry the same magnitude of charge on each plate.

Equivalent capacitance: parallel ● (core concept) — C_eq = ΣC_i: capacitors in parallel add directly, since each sees the full potential difference.

RC time constant ● (core concept) — τ = R_eqC_eq: the characteristic time for a capacitor to charge or discharge. A charging capacitor reaches about 63% of its final charge in one time constant; a discharging one falls to about 37% of its initial charge.

Charging a capacitor (qualitative) ● (core concept) — An uncharged capacitor placed in a circuit initially acts like a wire, letting charge flow easily. As it charges, the potential difference across it grows, the branch current falls, and the stored energy grows — all approaching steady state asymptotically. Descriptions are qualitative; only initial and final states are treated mathematically.

Steady state of an RC circuit ● (core concept) — After a time much longer than the time constant, a charging capacitor is fully charged (maximum potential difference, zero branch current) and a discharging capacitor is fully discharged; the branch can then be modeled with steady-state conditions.

Capacitor as open circuit at steady state ● (core concept) — A fully charged capacitor in a DC circuit carries no current in its branch, so the branch behaves as an open circuit. Only the initial (uncharged, acts like a wire) and final (fully charged, acts open) states are analyzed mathematically.