Unit 3: Electric Circuits

Circuit

A closed conducting path that allows electric charges to move under the influence of an electric field.

Voltage

The electric potential difference between two points; the “push” (energy per unit charge) that can drive current, measured in volts (V).

Electric potential difference (ΔV)

Change in electric potential energy per unit charge between two points: ΔV = ΔU/q.

Current (I)

Rate of flow of electric charge through a cross-section: I = dQ/dt, measured in amperes (A).

Charge (Q)

Amount of electric charge (the “how much”); current describes how fast charge flows (the “how fast”).

Conventional current direction

Defined as the direction positive charge would move; in metal wires electrons drift opposite this direction.

Electron drift

The slow net motion of electrons in a conductor under an electric field; typically opposite conventional current and not a “racing” motion around the circuit.

Direct current (DC)

Current that flows in only one direction (does not reverse).

Alternating current (AC)

Current that periodically reverses direction (often sinusoidal in time).

Frequency (f)

Number of cycles per second in an AC signal, measured in hertz (Hz).

Resistance (R)

Opposition to the flow of electric current; measured in ohms (Ω).

Ohmic (ideal) resistor

A resistor that obeys V = IR over its operating range (linear V–I relationship).

Ohm’s law

For an ohmic element, the relationship between voltage, current, and resistance: V = IR (not universal for all devices).

Resistivity (ρ)

Material property that quantifies how strongly a material resists current flow; used in R = ρL/A.

Wire resistance model (R = ρL/A)

Resistance of a uniform wire depends on material resistivity ρ, length L, and cross-sectional area A: R = ρL/A.

Power (P) in circuits

Rate of energy transfer or conversion in a circuit; measured in watts (W), where 1 W = 1 J/s.

Power relation (P = IV)

Electric power delivered to or dissipated by an element equals current times voltage: P = IV.

Power in a resistor (P = I²R)

Using Ohm’s law for a resistor: P = I²R (useful when current is known/held constant).

Power in a resistor (P = V²/R)

Using Ohm’s law for a resistor: P = V²/R (useful when voltage is known/held constant).

Electrical energy (E = Pt)

Energy delivered or dissipated over time t: E = Pt.

Impedance (Z)

Total opposition to AC current including resistance and reactive effects from capacitance and inductance; measured in ohms (Ω).

EMF (electromotive force, ℰ)

Energy per unit charge supplied by a source: ℰ = W/q; measured in volts and is not literally a force.

Internal resistance (r)

A real battery’s effective series resistance; causes a voltage drop Ir when current flows.

Terminal voltage

Actual measured voltage across a real battery’s terminals when delivering current: V_terminal = ℰ − Ir.

Open circuit

A condition with no current (I = 0); for a battery, V_terminal = ℰ.

Short circuit

External resistance near zero; current can become very large (approximately I ≈ ℰ/r for a real source), making it dangerous.

Ammeter

Device to measure current; placed in series and ideally has negligible resistance.

Voltmeter

Device to measure potential difference; placed in parallel and ideally has extremely large resistance.

Multimeter

Instrument that can measure voltage, current, and resistance (commonly used for troubleshooting and continuity checks).

Oscilloscope

Instrument that displays voltage versus time, used to analyze time-varying waveforms.

Function generator

Device that outputs test waveforms (e.g., sine, square, triangle) for circuit testing.

Logic analyzer

Tool that captures and analyzes digital signals (logic-level waveforms).

Power supply (laboratory)

Source that provides a controlled constant voltage or constant current for testing circuits.

LCR meter

Instrument that measures inductance (L), capacitance (C), and resistance (R).

Node

Point where two or more elements connect; ideal wires make all points on a node the same electric potential.

Branch

A path between nodes that contains one or more circuit elements.

Loop

Any closed path through a circuit used for loop (energy) equations.

Series connection

Components connected end-to-end with only one path for current; all series elements carry the same current.

Parallel connection

Components connected to the same two nodes; all parallel branches share the same voltage.

Equivalent resistance in series

Total resistance for series resistors adds: R_eq = R1 + R2 + …

Equivalent resistance in parallel

For parallel resistors: 1/Req = 1/R1 + 1/R2 + …; Req is less than the smallest branch resistance.

Capacitor

Component that stores energy in an electric field between conductors separated by an insulator.

Capacitance (C)

Measure of how much charge a capacitor stores per volt; measured in farads (F).

Capacitor charge–voltage relation (Q = CΔV)

Charge stored on a capacitor is proportional to the voltage across it: Q = CΔV.

Capacitor current relation (I = C dV/dt)

For constant C, capacitor current equals capacitance times the rate of change of capacitor voltage: I = C(dV/dt).

Energy stored in a capacitor

Stored electric-field energy: U = (1/2)CV² (also equals (1/2)QV or Q²/(2C)).

Time constant (τ)

Characteristic time scale for an RC circuit: τ = RC; sets the rate of exponential charging/discharging.

RC charging curve

For a series RC with an uncharged capacitor: VC(t) = ℰ(1 − e^(−t/RC)), I(t) = (ℰ/R)e^(−t/RC); at t = τ, VC ≈ 63.2% of final.

RC discharging curve

For discharge from initial V0 (no source): VC(t) = V0 e^(−t/RC), I(t) = (V0/R)e^(−t/RC); at t = τ, VC ≈ 36.8% of initial.

Kirchhoff’s rules

Conservation laws for circuits: junction rule (KCL) says the algebraic sum of currents at a node is zero (current in = current out); loop rule (KVL) says the algebraic sum of potential changes around any closed loop is zero (with consistent sign conventions).