Short on time? This page is the recap. For Figures 1–3 and the worked examples, use the full study guide. This guide is for the calculus-based course.
Recap
- A circuit is built from elements (wires, batteries, resistors, bulbs, capacitors, inductors, switches, ammeters, voltmeters) joined in one or more closed loops.
- A closed loop is a path that returns to its start without passing any point twice.
- An element carries a steady current only if it is in a closed loop that contains a source and has a potential difference across it.
- A single element can belong to several loops, so one change (a switch, a short) can affect several parts of the circuit.
- A schematic shows what is connected to what, not where things physically sit.
- Current on schematics is conventional current unless a question says otherwise: out of the + terminal, round the circuit, into the − terminal.
Key definitions and symbols
| Term or symbol | Meaning |
|---|---|
| Closed circuit | Charge can flow round a complete loop |
| Open circuit | A break (open switch, broken filament) stops the flow; I = 0 in that path |
| Short circuit | A path where charge can flow with no change in potential; elements across it carry no current |
| Battery symbol | Two unequal parallel lines; the long line is + |
| Capacitor symbol | Two equal parallel lines |
| Resistor / bulb | Zigzag / circle with a filament |
| Inductor | A row of loops (coil) |
| Ammeter / voltmeter | Circle with A / circle with V |
| Variable element | Diagonal arrow drawn through the symbol |
| Junction | A dot where wires connect |
Assumptions
- Connecting wires are ideal: no change in potential along them.
- “Lit” means there is a current in the bulb.
Mistakes to avoid
- Mixing up open and short. Open: no path. Short: an easy path with no potential change.
- Missing loops. List every closed path systematically; an element often sits in more than one.
- Battery vs capacitor symbol. Unequal lines vs equal lines.
- Current from the − terminal. That is electron flow, not conventional current.
- “Current gets used up.” In one loop, the current is the same at every point.
Quick self-check
- A wire joins the two ends of a lit bulb. What happens to the bulb? (It goes out: no potential difference across it)
- A battery and two bulbs are all connected between the same two junctions. How many closed loops are there? (3: any two of the three paths)
- A steady 0.40 A flows for 5.0 s in a closed loop. How much charge passes any point? (2.0 C)
Next: practice questions.