Historical Context & Motivation
Humans have been fascinated by electricity for thousands of years, from the ancient Greeks who rubbed amber to produce static sparks, to modern engineers designing circuits that fit on a fingernail. The journey from curiosity to mastery required centuries of painstaking experimentation. Understanding electric current — the orderly movement of charged particles through a conductor — transformed the way civilizations generate light, communicate, and compute.
These breakthroughs raised a central question that still drives IB Physics today: when billions of tiny charged particles drift through a wire, how do we describe, measure, and predict their collective behaviour? That question sits at the heart of Topic B.5 — Current and circuits.
Core Principles & Definitions
Before we dive into calculations, we need a solid vocabulary. Every circuit problem in IB Physics relies on a handful of core ideas, each linked to the particulate nature of matter. Charges do not appear from nowhere — they are real particles (usually electrons in metals) pushed along by energy sources. The concepts below form the foundation for everything else in this topic.
Electric Current (I)
Potential Difference (V)
Resistance (R)
Electromotive Force (emf, ε)
Internal Resistance (r)
Visual Explanation — A Simple Circuit
The diagram below shows a basic circuit with a battery of emf ε, internal resistance r, and an external resistor R. Study it carefully — this single-loop circuit is the starting point for nearly every IB circuit problem. Pay attention to the direction of conventional current (from the positive terminal through the external circuit and back to the negative terminal) and notice how the battery's internal resistance is drawn as a separate component inside the battery.
In this diagram, the current I flows out of the positive terminal, through the external resistor R, and returns to the negative terminal. Inside the battery, energy is supplied to the charges (that is what emf means), but some of that energy is dissipated across the internal resistance r. The relationship ε = I(R + r) captures the entire energy story of this loop. When the current is zero (open circuit), the terminal voltage equals ε. When the current is large, the voltage "lost" across r becomes significant.
Mathematical Framework
IB Physics B.5 requires you to work fluently with several equations connecting current, voltage, resistance, and power. Below are the essential relationships you need to know, along with clear definitions of every variable.
Detailed Breakdown — Series & Parallel Circuits
Understanding the difference between series and parallel configurations is one of the most important skills in circuit analysis. The diagram below compares the two side by side, clearly showing how current and voltage behave differently in each arrangement.
In a series circuit, there is only one path for the current to follow. Every charge must pass through every component, so the current is the same everywhere in the loop. The voltage, however, is shared — each resistor "uses up" a fraction of the total voltage proportional to its resistance.
In a parallel circuit, the current has multiple paths. At each junction, the current splits so that more current flows through the lower-resistance branch. The voltage across every parallel branch is the same because each branch connects directly to the same two nodes. Adding more resistors in parallel actually decreases the total resistance, because you are giving the current more paths to follow.
Worked Example — Circuit with Internal Resistance
A battery has an emf of 12.0 V and an internal resistance of 0.50 Ω. It is connected to two resistors: R₁ = 4.0 Ω and R₂ = 6.0 Ω in series. Find (a) the current in the circuit, (b) the terminal voltage of the battery, and (c) the power dissipated in R₂.
Strengths & Limitations of Circuit Models
The simple Ohm's law model and Kirchhoff's rules form an incredibly powerful toolkit for analysing DC circuits, but they do have boundaries. Knowing when a model breaks down is just as important as knowing how to apply it.
| Feature | Strengths | Limitations |
|---|---|---|
| Ohm's Law (V = IR) | Simple, powerful for ohmic conductors; quick calculations in exam settings. | Only applies to ohmic materials. Filament lamps, diodes, and thermistors have non-linear V–I relationships. |
| Kirchhoff's Junction Rule | Based on conservation of charge — universally valid for any circuit. | Requires careful identification of all branches; complex circuits lead to many simultaneous equations. |
| Kirchhoff's Loop Rule | Based on conservation of energy — works for any closed loop in any circuit. | Sign conventions can be confusing; breaks down at very high frequencies where electromagnetic wave effects matter (AC circuits). |
| Internal Resistance Model | Explains why real batteries behave differently from ideal ones; predicts terminal voltage accurately. | Assumes r is constant, but in reality internal resistance can change with temperature and age of the battery. |
Connection to Advanced Theory
The ideas in B.5 form a springboard to more advanced electrical physics. In later IB topics and at university level, you will encounter alternating current (AC), capacitors, inductors, and semiconductor devices — all of which build on the same conservation principles you have learned here.
| B.5 Concept | Advanced Extension |
|---|---|
| DC current (steady flow) | AC current — sinusoidal variation; introduces impedance and phase. |
| Resistance (R = V/I) | Conductivity — the reciprocal of resistivity; used extensively in semiconductor physics and materials science. |
| Simple series/parallel circuits | Complex networks — Wheatstone bridges, potential dividers, and nodal analysis. |
| Power dissipation (P = IV) | Energy storage — capacitors store energy in electric fields; inductors store energy in magnetic fields. |
| Ohmic conductors | Non-ohmic devices — diodes, LEDs, thermistors, and LDRs with non-linear V–I characteristics. |
The particulate view of current connects directly to the drift velocity model that underpins the equation I = nAvq, which you have already studied in this lesson. At a deeper level, quantum mechanics explains why different materials have different resistivities and why resistance in metals increases with temperature — more atomic vibrations mean more collisions for drifting electrons, reducing their drift velocity and thus the current for a given applied voltage.
Practice Problems
Lesson Summary
Electric current is the rate of flow of charge (I = ΔQ/Δt), measured in amperes. In metals, the charge carriers are electrons, connecting this topic to the particulate nature of matter. At a microscopic level, current is described by the drift velocity equation I = nAvq, where n is the number density of charge carriers, A is the cross-sectional area, v is the drift velocity, and q is the charge per carrier. The resistance of a conductor depends on its material, length, and cross-section through resistivity: R = ρL/A. Ohm's law (V = IR) relates voltage, current, and resistance for ohmic conductors, while Kirchhoff's rules — the junction rule (conservation of charge) and the loop rule (conservation of energy) — allow systematic analysis of any circuit.
Real batteries have internal resistance (r), so the terminal voltage is always less than the emf when current flows: V = ε − Ir. In series circuits, current is the same through all components and voltages add. In parallel circuits, voltage is the same across all branches and currents add. Power dissipated by a component is P = IV = I²R = V²/R. Together, I = nAvq, R = ρL/A, Ohm's law, Kirchhoff's rules, and the internal resistance equation form the complete toolkit for IB Physics B.5.