4.1 Current and Resistance

Current: the flow of charge

Electric current (I) is the rate at which charge flows past a point: I = dq/dt, measured in amperes (A). Conventionally, current direction is defined as the direction positive charge would move, even though it's usually electrons (negative) flowing the opposite way. Current is a scalar, but it flows through a defined cross-section of a conductor.

Current density and drift velocity

Current density (J) relates current to the conductor's cross-sectional area: J = I/A. Microscopically, J = nqv_d, where n is charge carrier density, q is charge per carrier, and v_d is drift velocity — the slow net velocity of carriers superimposed on their random thermal motion. This connects macroscopic current to microscopic charge motion.

Resistance and resistivity

Resistance (R) opposes current flow, defined by Ohm's Law: V = IR, measured in ohms (Ω). Resistance depends on material and geometry: R = ρL/A, where resistivity (ρ) is an intrinsic material property, L is length, and A is cross-sectional area. Longer, thinner wires have more resistance; resistivity increases with temperature for most conductors.

Key terms

Electric current (I)

Rate of charge flow: I = dq/dt, measured in amperes (A).

Current density (J)

Current per unit cross-sectional area: J = I/A = nqv_d.

Drift velocity (v_d)

The small net velocity of charge carriers in the direction of current flow, caused by an applied electric field.

Ohm's Law

V = IR — voltage equals current times resistance.

Resistivity vs. Resistance

Resistivity (ρ) is an intrinsic material property; resistance (R = ρL/A) also depends on the conductor's length and cross-sectional area.

Try an AP-style question

A current of 3 A flows through a wire of cross-section 1.5 × 10⁻⁶ m². What is the current density?

1. 2 × 10⁶ A/m²
2. 5 × 10⁻⁷ A/m²
3. 3 A/m²
4. 4.5 × 10⁻⁶ A/m²