B.5 Current and circuits

UNIT SYLLABUS

SL/HL 6 hours

Electric circuits are controlled rivers of charge. A cell's emf sets the energy given to each coulomb; resistance determines how the current responds ($R = V/I$); and resistivity separates what is due to the material from what is due to geometry ($\rho = RA/L$). The series and parallel rules — same current versus same voltage — let you reduce any resistor network step by step, and the internal resistance of real cells explains why a battery's terminal voltage sags under load. Power dissipation ($P = VI = I^2R = V^2/R$) connects the circuit diagram to heat, light and your electricity bill.

Guiding Questions

? How do charge carriers move through circuits, and what determines the current?
? How can circuit laws be used to predict the behaviour of networks of components?

✓ What the IB expects you to master

Describe cells (chemical and solar) as sources of emf, and interpret circuit diagrams.
Define current as rate of flow of charge, $I = \Delta q/\Delta t$ , and potential difference as work per unit charge, $V = W/q$ .
Explain conduction and insulation via mobility of charge carriers, and the origin of resistance.
Use $R = V/I$ , resistivity $\rho = RA/L$ , and Ohm's law; distinguish ohmic from non-ohmic behaviour (including the heating of a filament).
Calculate power dissipation: $P = VI = I^2R = V^2/R$ .
Combine resistors: series $R_s = R_1 + R_2 + \ldots$ (same current), parallel $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$ (same voltage).
Account for internal resistance with $\varepsilon = I(R + r)$ , and understand variable resistance (potentiometers, thermistors, LDRs).

1 Key Formulas

Electric current

I = \frac{\Delta q}{\Delta t}

Potential difference

V = \frac{W}{q}

Resistance

R = \frac{V}{I}

Resistivity

\rho = \frac{RA}{L}

Electrical power

P = VI = I^{2}R = \frac{V^{2}}{R}

Resistors in series

R_{s} = R_{1} + R_{2} + \ldots

Resistors in parallel

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \ldots

EMF and internal resistance

\varepsilon = I(R + r)

2 Exam Preparation & Topic Explanations

Circuit reduction discipline

Redraw before you calculate. Collapse obvious series and parallel groups step by step, labelling each intermediate resistance, until one resistor remains; find the total current; then expand back outwards, assigning currents and voltages at each step.

For internal-resistance experiments, the V–I graph of a real cell is a straight line: intercept = emf, gradient = $-r$ . This is a named practical — know the method and the graph.

Pro Exam Strategy

Series: same current, voltages add. Parallel: same voltage, currents add. Say it before every problem.
Adding a resistor in parallel always REDUCES total resistance — check answers against this instinct.
Use the $P$ form that avoids what you don't know: $I^2R$ in series chains, $V^2/R$ across parallel branches.
Non-ohmic I–V curves: filament bends towards the V-axis (R rising); the guide expects you to explain why via lattice vibrations.

3 MCQ Practice

Q1. Two identical resistors connected in parallel have combined resistance $R_p$ . Connected in series, their combined resistance is:

$R_p$
$2R_p$
$4R_p$
$R_p/4$

Q2. A battery of emf 12 V and internal resistance $0.50\ \Omega$ delivers a current of 4.0 A. Its terminal potential difference is:

12 V
10 V
14 V
8.0 V

Q3. The current through a filament lamp doubles when the potential difference across it is tripled. The lamp is:

Ohmic, because current increases with voltage
Non-ohmic, because resistance has increased with temperature
Non-ohmic, because resistance has decreased with temperature
Ohmic, because the filament obeys $P = VI$

4 Short Answer Questions

PDF

Download the practice worksheet

All questions from this unit + answer key — free, printable.

↓

Formula Booklet →

Every data-booklet equation, searchable.

Simulations →

See this physics in motion.

Daily Question →

Practise one concept a day.

← Previous unit

B.4 Thermodynamics

Next unit →

C.1 Simple harmonic motion

Stuck on Current and circuits?

Get it explained properly — 1-on-1, by a specialist who has taught this unit for 13+ years. Newtonine students average 6.8 in IB Physics.

Book a Free Consultation