Physics C: E&M · Unit 3: Electric Circuits · 14 min read · Updated 2026-05-11
Current and Resistance — AP Physics C: Electricity and Magnetism
AP Physics C: Electricity and Magnetism · Unit 3: Electric Circuits · 14 min read
1. Electric Current, Drift Velocity, and Current Density★★☆☆☆⏱ 4 min
Electric current is the foundational quantity for all circuit analysis, describing net charge flow through a cross-sectional surface. AP Physics C exclusively uses **conventional current** convention, where current direction matches the flow of positive charge, opposite to the direction of electron flow in metallic conductors.
I = \frac{dQ}{dt}
For uniform current flow through a conductor of constant cross-sectional area $A$, we define current density $\vec{J}$, a vector pointing in the direction of conventional current. Microscopically, when an electric field is applied to a conductor, free charges accelerate then scatter off the crystal lattice, resulting in a net average velocity called drift velocity $v_d$. For a material with $n$ charge carriers per unit volume, each of charge $q$, we derive the relation:
J = n q v_d \implies I = n q v_d A
Exam tip: If a question asks for the direction of current, always give the conventional direction (opposite to electron drift velocity). AP exam graders will deduct points for giving electron direction unless explicitly asked.
2. Resistance, Resistivity, and Ohm's Law★★☆☆☆⏱ 4 min
Resistivity is an intrinsic material property that describes how strongly a material opposes current flow. Resistance is an extrinsic property that depends on both the material's resistivity and the size/shape of the conductor.
R = \rho \frac{L}{A}
Where $L$ is the length of the conductor along the direction of current flow, and $A$ is the cross-sectional area perpendicular to current flow. Ohm's law is an empirical law that only applies to ohmic materials, where potential difference is proportional to current. A common misconception is that $R = V/I$ is Ohm's law: this is just the definition of resistance at a given operating point, which holds even for non-ohmic materials like diodes.
V = I R
Exam tip: AP MCQ distractors almost always include the answer you get from leaving length/area units in centimeters. Always convert to meters before calculating resistance, and do a quick unit check to catch this mistake.
3. Temperature Dependence of Resistance★★★☆☆⏱ 3 min
Resistivity depends on temperature because higher temperatures increase lattice vibrations in metals, leading to more scattering of charge carriers and higher resistivity. For small temperature changes, we use a linear empirical relation that applies to both resistivity and total resistance:
R(T) = R_0 \left[1 + \alpha (T - T_0)\right]
Where $R_0$ is resistance at reference temperature $T_0$ (usually $20^\circ\text{C}$), and $\alpha$ is the temperature coefficient of resistivity. For metals, $\alpha$ is positive (resistance increases with temperature); for semiconductors, $\alpha$ is negative (resistance decreases with increasing temperature).
4. Power Dissipation (Joule Heating) & Combined Applications★★★☆☆⏱ 3 min
Power dissipated as heat in a resistive material comes from the work done by the electric field on moving charge carriers. Starting from $P = dU/dt = V dQ/dt = VI$, we can rewrite this into three equivalent forms using Ohm's law:
P = VI = I^2 R = \frac{V^2}{R}
Common Pitfalls
Why: Students confuse the microscopic motion of negative electrons with the AP convention of conventional current
Why: Students confuse the definition of resistance at an operating point with Ohm's law, which requires proportionality between $V$ and $I$ across all operating points
Why: Students mix up the surface area of the wire with the cross-sectional area perpendicular to current flow
Why: Students mix up intrinsic resistivity and extrinsic resistance
Why: Students focus on the obvious length change and miss that stretching reduces cross-sectional area to keep volume constant