Theme B · Particulate Nature of Matter · SL + HL · 6 hours

B.5 Current and Circuits

How do charged particles flow through materials, and what are the consequences of resistance?

Current is the flow of charge carriers — electrons in metals, ions in electrolytes, and holes in semiconductors. The rate of flow, measured in amperes, is charge per unit time. Potential difference is the energy per unit charge available to drive that flow; resistance is the opposition to it. Ohm's law — V = IR — holds for metallic conductors at constant temperature, but not for all materials or all conditions.

Internal resistance is the part of Ohm's law that textbooks gloss over but real circuits cannot ignore. Every cell has an internal resistance r; when current flows, some of the EMF is "used up" driving current through the cell itself, so the terminal voltage is always less than the EMF. Understanding this is essential for analysing real circuits, where the battery is not an ideal voltage source.

A battery of EMF 12 V and internal resistance 0.8 Ω is connected to an external resistor of 3.2 Ω. Calculate the current, the terminal voltage of the battery, and the power dissipated in the external resistor. What fraction of the total power is wasted in the internal resistance?

Key equations

Current: I = Δq/Δt
Potential difference: V = W/q
Resistance: R = V/I; Resistivity: ρ = RA/L
Power: P = IV = I²R = V²/R
Series: Rs = R₁ + R₂; Parallel: 1/Rp = 1/R₁ + 1/R₂
EMF and internal resistance: ε = I(R + r); terminal voltage = ε − Ir

What students must understand

Linking questions

Practice worksheets

Labs

Video Support

Khan Academy
Electric circuits (part 1)
Electric circuits (part 2)
Flipping Physics
Electric Circuit Basics
Resistance and Ohm's Law
The Organic Chemistry Tutor
Electric Current & Circuits Explained, Ohm's Law, Charge, Power, Physics Problems, Basic Electricity
Kirchhoff's Law, Junction & Loop Rule, Ohm's Law - KCl & KVl Circuit Analysis - Physics
Ohm's Law
Michel van Biezen
Physics 42 Ohm's Law and Resistor Circuits (1 of 23) Series and Parallel
Electrical Engineering: Basic Laws (2 of 31) Ohm's Law
WNY Tutor — worked problems
Two resistors connected in series have an equivalent resistance of 690 Ω
Using Kirchhoff's rules find the current in each resistor
Physics with Professor Matt Anderson — full course modules
Module 21 | Current | Physics with Professor Matt Anderson
Module 22 | DC Circuits | Physics with Professor Matt Anderson
WNY Tutor — worked-problem sets
Current and Resistance