IGCSE Physics: Electricity, Magnetism and Atomic Physics

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IGCSE Physics: Electricity, Magnetism and Atomic Physics

TL;DR

You'll be able to calculate current, voltage and resistance in series and parallel circuits, explain how motors and generators use magnetic force and induction, and work out how much of a radioactive sample remains after a given time. These three areas supply a huge share of calculation marks on the exam.

1. The Mental Model

Electricity is just charge flowing because something pushes it — voltage is the push, resistance is the friction, current is the flow rate. Magnetism and electricity are two sides of one effect: moving charge makes a field, and a changing field pushes charge. Atoms fall apart in fixed, random-but-predictable ways, and we measure that randomness using half-life. If you remember that voltage pushes, resistance resists, and fields and currents always create each other, you can derive almost every formula in this topic instead of memorising it.

2. The Core Material

2.1 Circuits: Ohm's Law, Series and Parallel

The foundation formula is:

$$V = IR$$

where $V$ is potential difference (volts), $I$ is current (amps), $R$ is resistance (ohms). Power delivered is:

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

Use whichever form avoids a value you don't know.

Series circuits — one path, so current is the same everywhere, and voltages add up:

$$I_{\text{total}} = I_1 = I_2 = I_3, \qquad V_{\text{total}} = V_1 + V_2 + V_3$$
$$R_{\text{total}} = R_1 + R_2 + R_3$$

Parallel circuits — multiple paths, so voltage is the same across each branch, and currents add up:

$$V_{\text{total}} = V_1 = V_2 = V_3, \qquad I_{\text{total}} = I_1 + I_2 + I_3$$
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

Key exam insight: adding resistors in series always increases total resistance, but adding them in parallel always decreases it (you've given the current more routes). A common check: in parallel, $R_{\text{total}}$ must always be smaller than the smallest individual resistor.

2.2 Magnetism: The Motor Effect and Electromagnetic Induction

A current-carrying wire in a magnetic field feels a force (the motor effect):

$$F = BIL$$

where $B$ is magnetic flux density (tesla), $I$ is current, $L$ is the length of wire in the field. The direction comes from Fleming's left-hand rule: thumb = thrust (force), First finger = Field, seCond finger = Current.

Run the process backwards and you get a generator: moving a wire (or coil) through a magnetic field induces an EMF — this is electromagnetic induction. The size of the induced EMF increases if you: move the magnet/coil faster, use a stronger magnet, or add more coil turns. Lenz's Law tells you the direction: the induced current always opposes the change that caused it (so you have to do work to keep the motion going — this is why dynamos get harder to turn the more electricity they supply).

Transformers use this same principle with an alternating current creating a changing magnetic field in an iron core, which induces a voltage in a second coil:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

where $N_p$, $N_s$ are the number of turns on the primary and secondary coils. For an ideal (100% efficient) transformer, power in = power out, so $V_p I_p = V_s I_s$ — this is why step-up transformers raise voltage but lower current, which is why power is transmitted at high voltage over long cables (lower current means lower heat loss, $P = I^2R$).

flowchart LR
    A["Coil moves through magnetic field (or field changes)"] --> B["Magnetic flux linking the coil changes"]
    B --> C["EMF is induced in the coil (Faraday's Law)"]
    C --> D["Induced current flows if circuit is closed"]
    D --> E["Induced current creates its own field opposing the change (Lenz's Law)"]
    E --> F["Extra force needed to keep moving the coil = energy input converted to electrical energy"]

2.3 Atomic Structure and Radioactive Decay

An atom has a nucleus (protons + neutrons) surrounded by electrons. The nucleon number (mass number, $A$) is protons + neutrons; the proton number (atomic number, $Z$) is protons alone. Isotopes share $Z$ but differ in $A$.

Unstable nuclei emit radiation to become more stable:

Decay equations must balance both $A$ and $Z$ on each side. For alpha decay:

$$^{A}_{Z}X \rightarrow\ ^{A-4}_{Z-2}Y + \ ^{4}_{2}\text{He}$$

For beta decay, a neutron turns into a proton + electron, so $A$ stays the same but $Z$ increases by 1:

$$^{A}_{Z}X \rightarrow\ ^{A}_{Z+1}Y + \ ^{0}_{-1}e$$

Half-life is the time for half the undecayed nuclei (or half the activity) to decay:

$$N = N_0 \left(\frac{1}{2}\right)^{t / t_{1/2}}$$

This is random at the level of individual atoms but totally predictable in large numbers — that's the key conceptual point examiners love to test with "explain why we cannot predict when one particular atom will decay" questions.

3. Worked Example

Circuit problem: A 6 V battery is connected to a 4 Ω resistor in series with a parallel combination of a 6 Ω and a 3 Ω resistor. Find (a) the total resistance, (b) the total current, (c) the current through the 3 Ω resistor, (d) the total power delivered by the battery.

(a) Parallel section first:
$$\frac{1}{R_p} = \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} \implies R_p = 2\ \Omega$$

Add the series resistor:
$$R_{\text{total}} = 4 + 2 = 6\ \Omega$$

(b) Total current using Ohm's Law on the whole circuit:
$$I = \frac{V}{R} = \frac{6}{6} = 1\ \text{A}$$

(c) Voltage across the parallel section:
$$V_p = I \times R_p = 1 \times 2 = 2\ \text{V}$$

Current through the 3 Ω branch:
$$I_3 = \frac{V_p}{R_3} = \frac{2}{3} \approx 0.67\ \text{A}$$

(d) Total power delivered by the battery:
$$P = VI = 6 \times 1 = 6\ \text{W}$$

Check: current through the 6 Ω branch is $2/6 = 0.33$ A, and $0.67 + 0.33 = 1$ A — matches the total current, confirming the answer is consistent.

4. Examiner's Breakdown

4.1 What Examiners Actually Reward

1. "Current is the same at every point in a series circuit because there is only one path for charge to flow."
2. "The potential difference across each branch of a parallel circuit is the same because each branch is connected directly across the supply."
3. "The induced current opposes the change that caused it (Lenz's Law), which is why work must be done to move the conductor."
4. "Total resistance in parallel is always less than the smallest individual resistance because extra paths are provided for current."
5. "It is impossible to predict exactly when an individual unstable nucleus will decay; decay is random, but with a very large number of nuclei the overall activity follows a predictable pattern."
6. "In an ideal transformer, power input equals power output, so a step-up in voltage must give a step-down in current."

4.2 Trapdoor Mistakes

1. MISTAKE: Adding resistors in parallel using $R_{\text{total}} = R_1 + R_2$. → FIX: Use $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}$, then flip the final answer.
2. MISTAKE: Saying beta decay changes the nucleon number. → FIX: State that nucleon number ($A$) stays the same in beta decay; only proton number ($Z$) increases by 1, because a neutron converts to a proton and an electron.
3. MISTAKE: Writing "half-life is the time for all the substance to decay." → FIX: "Half-life is the time for half of the remaining undecayed nuclei to decay" — it's always about what's left, not the original amount.
4. MISTAKE: Using Fleming's right-hand rule for the motor effect. → FIX: Left-hand rule is for force/motors; right-hand rule (dynamo rule) is for generators/induction — mixing these up loses easy direction marks.

4.3 Score-Boosting Comparisons