Electric circuits

What the exam asks

Expect a circuit diagram, two or three numbers, and no calculator. The items are: find the total resistance, find the current through or the voltage across one named component, work out what changes when a switch closes or a component is added, and rank lamps by brightness. V = IR is assumed knowledge and will not be printed. The trap that decides most of these is swapping the two sharing rules: writing the same current through two parallel branches, or the same voltage across two series resistors. Before any arithmetic, mark on the diagram what is shared and what divides, and the rest is division. The second trap is answering with the total current when the question asked about one branch, or with the emf when it asked for the terminal voltage. Both are numbers you worked out honestly on the way to the answer, which is exactly why they are offered as options.

This is the physics topic where you are most on your own. V = IR is one of the three formulae worth carrying in, which means the stem will not remind you of it and the question assumes you can reason from it, in your head, with no calculator.

Two rules organise everything else. In series there is one path, so the current is the same everywhere and the voltage divides between the components. In parallel the branches join the same two points, so the voltage across each is the same and the current divides between them. Holding this the wrong way round is the most expensive mistake in the topic, because it does not produce one wrong answer, it produces every wrong answer after it.

The rest is combinations of those two, plus the fact that a real cell has resistance of its own. When a question closes a switch, adds a lamp, or lays a wire across something, it is asking you to follow the change through in order: total resistance first, then the current the supply delivers, then back down into whichever branch was asked about.

What to hold

• In series the current is the same through every component, and the supply voltage divides between them in proportion to their resistances.
• In parallel the voltage across every branch is the same, and the current divides between the branches in inverse proportion to their resistances.
• Resistances in series add. Resistances in parallel combine as 1/R = 1/R1 + 1/R2, and the total is always smaller than the smallest branch.
• Adding a resistor in parallel lowers the total resistance, because it hands the current another path without altering the paths already there. More current for the same voltage, and V = IR with V fixed and I up, means R has gone down.
• A potential divider splits the supply voltage in the ratio of the two series resistances, so the larger resistor takes the larger share.
• In series the largest resistor dissipates the most power, because the current is common and P = I squared R. In parallel the smallest resistor dissipates the most, because the voltage is common and P = V squared / R.
• A real cell has internal resistance, so its terminal voltage V = emf - Ir falls as it delivers more current. The emf is what it would give at zero current.
• An ideal ammeter has zero resistance and goes in series. An ideal voltmeter has infinite resistance and goes in parallel. Each is built so as not to disturb the thing it is reading.
• The current into a junction equals the current out of it, which is conservation of charge. Round any loop the voltage rises equal the voltage drops, which is conservation of energy.
• Laying a wire across a resistor shorts it out: the combination has nearly zero resistance, the current bypasses the resistor, and the voltage across it collapses to almost nothing.
• Adding a lamp in series dims every lamp, because total resistance rises and the shared current falls. Adding a lamp in parallel leaves the others alone if the supply is ideal, and dims them slightly if it has internal resistance.