Current & Resistance
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Current is the rate charge flows, I = ΔQ/Δt. Resistance is how hard a component makes it to push current through: R = ρL/A for a wire, and ΔV = IR. Current isn’t used up going around a circuit; energy is.
1. The key equations
2. Wires, bulbs and meters
Resistance depends on area, not diameter: double the diameter and A is 4 times larger, so R is ¼ as large.
A resistor that obeys Ohm’s law has a straight-line I–V graph. A lightbulb doesn’t: its filament heats up, its resistance rises, and the graph curves.
An ammeter goes in series and has almost zero resistance, so it doesn’t change the current.
A voltmeter goes in parallel and has a huge resistance, so almost no current goes through it.
3. Example, then try it
A nichrome wire (ρ = 1.1 × 10⁻⁶ Ω·m) is 2.0 m long with a cross-sectional area of 5.0 × 10⁻⁷ m². Find its resistance.
R = ρL/A = (1.1 × 10⁻⁶)(2.0) ÷ (5.0 × 10⁻⁷) = 4.4 Ω.
A battery with ε = 9.0 V and internal resistance 0.50 Ω is connected to a 4.0 Ω resistor. Find the current, the terminal voltage, and the charge that passes in 30 s.
Current: the resistances are in series: I = ε ÷ (R + r) = 9.0 ÷ 4.5 = 2.0 A.
Terminal voltage: ε − Ir = 9.0 − (2.0)(0.50) = 8.0 V, the same as IR = (2.0)(4.0).
Charge: ΔQ = IΔt = (2.0)(30) = 60 C.
Answer: 2.0 A; 8.0 V at the terminals; 60 C in 30 s.
4. Common mistakes
A wire of the same material and thickness is twice as long as another. How does its resistance compare?
R = ρL/A. Same ρ and A, double L, so double R.
Ready to practice?
5 questions on Current & Resistance, each with a hint and an explanation for every wrong answer.