AP Physics 2 Unit 3 Circuits: Building Intuition for Charge Flow and Opposition

Electric current

The rate at which electric charge passes through a chosen cross-section of a conductor (charge per unit time).

Average current (I = ΔQ/Δt)

Definition of current as the amount of charge ΔQ that crosses a cross-section during a time interval Δt.

Cross-section (in current problems)

An imaginary “gate” cutting across a conductor; current describes how much charge passes through that gate each second.

Conventional current direction

The defined direction of current as the direction positive charge would move (used consistently in circuit analysis).

Electron flow

In metal wires, the actual motion of electrons (negative charges), which is opposite the direction of conventional current.

Electric field in a conductor

A field established inside a wire when a potential difference is applied; it exerts force on charge carriers and causes drift motion.

Drift velocity

The small average net velocity of charge carriers in a conductor, superimposed on their random thermal motion.

Carrier-collision model (microscopic origin of resistance)

Frequent collisions of charge carriers with the lattice/impurities prevent continuous acceleration and lead to a steady drift speed and heating.

Current–drift relation (I = nqAv_d)

Relationship connecting current to microscopic motion: n (carriers/volume) × q (charge per carrier) × A (area) × v_d (drift speed).

Ampere (A)

Unit of current; 1 A = 1 C/s.

Coulomb (C)

Unit of electric charge used in circuit calculations; relates to current via 1 A = 1 C/s.

Ammeter

Device that measures current; it must be placed in series so the same current passes through the meter.

Series connection (for measuring current)

A connection where components share the same current; required placement for an ammeter.

Parallel ammeter mistake (short-circuit risk)

Placing an ammeter in parallel can effectively create a low-resistance path and short part of the circuit, giving incorrect/unsafe results.

Resistance

A measure of how strongly a component opposes current for a given potential difference; operationally R = ΔV/I (under steady conditions).

Ohm (Ω)

Unit of resistance; 1 Ω = 1 V/A.

Resistivity (ρ)

A material property describing how strongly the material resists current flow; independent of the object’s shape.

Wire resistance formula (R = ρL/A)

For a uniform conductor: resistance increases with length L and resistivity ρ, and decreases with cross-sectional area A.

Conductivity (σ)

Material property defined as σ = 1/ρ; higher conductivity means charge moves more easily.

Temperature dependence of metal resistance

For metals, resistance typically increases as temperature increases due to increased lattice vibrations and collisions.

Ohm’s law (ΔV = IR)

Linear relationship between potential difference across an element and current through it; valid when the element behaves ohmically (constant R).

Ohmic device

A device for which ΔV is proportional to I (constant resistance); ΔV vs I graph is a straight line through the origin.

Non-ohmic device

A device with a non-linear ΔV–I relationship (resistance changes with conditions), e.g., diodes or incandescent bulbs.

Resistance from graph slope

On a ΔV (vertical) vs I (horizontal) graph, slope = ΔV/I = R; on an I vs ΔV graph, slope = I/ΔV = 1/R.

Electrical power in a circuit element

Rate of electrical energy transfer: P = IΔV; for an ohmic resistor, also P = I^2R and P = (ΔV)^2/R.