AP Physics C: Unit 3 — Circuit Fundamentals

Electric Current

The rate at which charge flows through a cross-sectional area of a conductor.

Instantaneous Current

Defined using calculus as I = dQ/dt for variable charge flow.

Unit of Electric Current

Ampere (A), where 1 A = 1 C/s.

Direction of Current

Conventional current flows from high potential to low potential.

Drift Velocity

The average velocity of charge carriers, such as electrons, in a conductor.

Current Density

A vector quantity that describes the flow of charge per unit area at a specific point.

Resistivity

A material property that quantifies how strongly a material opposes the flow of electric current.

Resistance

A measure of how difficult it is for current to pass through a specific component.

Ohm's Law

Empirical relationship stating that V = IR for Ohmic materials.

Conductivity

Reciprocal of resistivity, defined as σ = 1/ρ.

Temperature Dependence of Resistivity

Resistivity usually increases with temperature in metals due to increased atomic collisions.

Volume Conservation in Resistance Calculation

If the length of a wire doubles and volume remains constant, the cross-sectional area halves.

Electromotive Force (EMF)

The maximum potential difference supplied by a source when no current is flowing.

Internal Resistance

Resistance caused by the chemicals and materials inside a real battery.

Terminal Voltage

The actual voltage measured across the battery terminals when current flows.

Power Relationships

Equations relating power generated, dissipated, and delivered in electric circuits.

Current Conservation

Current entering a resistor equals the current leaving it; it is energy that drops.

Drift Velocity Misconception

Electrons move slowly (millimeters per second), while the electric field propagates near the speed of light.

Resistivity vs. Resistance Confusion

Resistivity (ρ) is a material constant, while Resistance (R) is a property of an object.

Significance of EMF

EMF is work per unit charge (Volts), representing the energy available for charge movement.

Graphing Ohm's Law

In a V (y-axis) vs I (x-axis) graph, the slope is R; in an I vs V graph, the slope is 1/R.

Cross-sectional Area (A)

The area through which current flows; affects the resistance of a conductor.

Charge Carrier Density (n)

Number of charge carriers per unit volume, measured in carriers/m³.

Ohm's Law Vector Form

For isotropic materials, the relation is given by E = ρJ or J = σE.

Energy Delivered to Load

Power delivered to load is V_ab I = E I - I²r.

Materials Classification

Materials can be classified as Ohmic (obey Ohm's Law) or non-Ohmic (do not).

Temperature Coefficient of Resistivity (α)

Parameter that quantifies how resistivity changes with temperature.