Model: each battery is an ideal source of the voltage you set, with the internal resistance you choose (0 = ideal). Each bulb is a fixed 6 Ω resistor (a “6 V, 6 W” bulb); its glow follows its power P = I²R, full glow at 6 W. Wires, closed switches and ammeters have (almost) zero resistance; the voltmeter is ideal and draws no current. Every number comes from Ohm’s law and Kirchhoff’s laws. The speed of the dots shows the size of the current, not the real speed of electrons (well under 1 mm per second).
Yellow dots: conventional current, from + to − through the circuit (and from − to + inside the battery).
The same bulbs and the same battery, connected two ways. In a series circuit everything is in one loop; in a parallel circuit each bulb has its own branch. Choose the number of bulbs, then tap a bulb to unscrew it and see what happens to the others.
| Series | Parallel | |
|---|---|---|
| Paths for the current | one loop | several paths, one through each branch |
| Current | the same everywhere: I = I1 = I2 | splits and adds up: I = I1 + I2 + … |
| Voltage | shared: V = V1 + V2 + … | the same across every branch: V = V1 = V2 |
| Total resistance | R = R1 + R2 + … (bigger than each) | 1/R = 1/R1 + 1/R2 + … (smaller than the smallest) |
| More identical bulbs | each bulb gets dimmer | each stays as bright (ideal battery); the battery gives more current |
| One bulb removed | all go out | the others stay on |
| Used in | switches and fuses (in series with what they control), simple torches | house lights and sockets, car lights |
A conductor lets electric current flow through it easily; an insulator does not. Clip a material into the gap at the bottom of this circuit (6 V battery, 6 Ω bulb, ammeter) and watch the bulb. Metals and graphite conduct; plastic, rubber, wood, glass, paper and cotton insulate.
In this model metals have practically zero resistance and the pencil lead is given 5 Ω (a real lead’s resistance depends on its length, thickness and hardness). Insulators are treated as a complete break. Never test mains electricity: only use a small battery.
Twelve circuit symbols you need to know, all in one working circuit: cell, battery, switches, lamp, LED, resistor, variable resistor, fuse, ammeter, voltmeter and junction. Scientists draw circuits with symbols because they are quick to draw and everyone reads them the same way. Switch between the labeled diagram, a blank one to test your memory, and a quiz where you place each label yourself. You can also download both versions or print a label worksheet.
Tap a word, then tap the numbered box it belongs to (on the diagram or in the list below). Tap a filled box to take the word back. On a phone, swipe the diagram sideways to see every number.
Ten questions from a bank of 24, from complete circuits to Ohm’s law calculations.
Tap a material, then tap the box it belongs in. Check when all twelve are placed.
Which kind of circuit does each statement describe? Sort all twelve.
A bulb lights only when there is an unbroken path from one end of the battery, through the bulb, and back to the other end. Any gap, such as an open switch, a loose wire or a piece of plastic, stops the current everywhere in that loop. That is an open circuit. Metals let current through easily (conductors); plastic, rubber, glass and wood do not (insulators), which is why wires are metal inside and plastic outside.
Put two bulbs one after the other in the same loop and they are in series: the same current goes through both, they share the battery’s voltage, and both are dimmer. Give each bulb its own branch and they are in parallel: each bulb gets the full voltage and shines as brightly as one bulb alone, and if one breaks the other stays on. An ammeter measures current and goes in series; a voltmeter measures voltage and goes across a part.
For a resistor at a steady temperature the current is proportional to the voltage: V = IR. So 6 V across 6 Ω gives 1 A. In series the resistances add (R = R1 + R2); in parallel 1/R = 1/R1 + 1/R2, so the total is smaller than any branch. The power a part uses is P = IV = I²R = V²/R. Two 6 Ω bulbs in series on 6 V carry 0.5 A each and use 1.5 W each, a quarter of the 6 W one bulb uses alone: that is why series bulbs are dim.
A real battery has an internal resistance r, so the voltage at its terminals falls as it gives more current: V = ε − Ir, where ε (the EMF) is the voltage with no current. Every circuit obeys Kirchhoff’s laws: the currents into a junction equal the currents out (charge is conserved), and the voltages around any closed loop add up to zero (energy is conserved). The lab solves every circuit you build with exactly these laws.
Load “Series: 2 bulbs” and unscrew one bulb. Then load “Parallel: 3 bulbs” and do the same. Load “Short across a bulb” and close the switch: why does bulb 1 get brighter? Finally load “Ohm’s law”, record the current at 1.5, 3, 4.5 and 6 V, and check that the graph is a straight line with a gradient of 1/R.
| Quantity | Symbol | Unit | What it means | Measured with |
|---|---|---|---|---|
| Current | I | ampere (A) | how much charge flows past a point each second (1 A = 1 coulomb per second) | ammeter, in series |
| Voltage (potential difference) | V | volt (V) | energy given to or taken from each coulomb of charge (1 V = 1 joule per coulomb) | voltmeter, in parallel (across the part) |
| Resistance | R | ohm (Ω) | how hard it is for current to flow; R = V ÷ I | ohmmeter, or work out V ÷ I |
| Power | P | watt (W) | energy transferred each second; P = IV | work out I × V |
| Charge | Q | coulomb (C) | Q = I × t | |
| Energy | E | joule (J) | E = P × t = Q × V |
Ohm’s law holds for metal wires and resistors kept at a constant temperature (ohmic conductors): their I–V graph is a straight line through the origin. A real filament lamp gets hotter as the current rises, so its resistance rises and its I–V graph curves; a diode only conducts one way. (In the lab the bulb is kept at a fixed 6 Ω so that the numbers are easy to follow.)
| Idea | Formula | Notes |
|---|---|---|
| Kirchhoff’s junction rule | ΣIin = ΣIout | charge is conserved at every junction |
| Kirchhoff’s loop rule | ΣV = 0 around any closed loop | energy is conserved; battery voltages are gains, voltages across resistors are drops |
| EMF and internal resistance | V = ε − Ir | set internal resistance in the lab to see the terminal voltage fall |
| Resistivity | R = ρL ÷ A | copper ρ ≈ 1.7 × 10−8 Ω m: 10 m of 1 mm² copper wire is only about 0.17 Ω, which is why wires count as zero resistance |
| Resistance and temperature | ρ(T) ≈ ρ0[1 + α(T − T0)] | metals: resistance rises when hot (filament lamps); a thermistor’s usually falls |
| Charging a capacitor (RC circuit) | VC = V0(1 − e−t/RC), τ = RC | 63% charged after one time constant; see the Capacitors and RC, RL, RLC Circuits simulations |
A complete, unbroken loop that electric current can flow around: a source such as a battery, wires, and parts such as bulbs, motors or buzzers. If there is a gap anywhere (an open switch, a broken wire, an insulator), the circuit is open and no current flows.
Key takeaway: no complete loop, no current.In a series circuit all the parts are in one loop, so the same current flows through each and they share the battery voltage. In a parallel circuit each part is on its own branch, so each gets the full battery voltage and the branch currents add up to the battery current.
Key takeaway: series = one path; parallel = several branches.Each extra bulb adds resistance, so the current round the loop falls, and the bulbs share the battery voltage. With two identical bulbs each gets half the voltage and half the current, so a quarter of the power.
Key takeaway: more series bulbs, less current, less power each.So that every light and socket gets the full mains voltage, each one can be switched on and off by itself, and one broken lamp does not turn everything else off. Switches and fuses are put in series with the thing they control.
Key takeaway: parallel: full voltage and independent control.For a conductor at constant temperature, the current is proportional to the voltage: V = I × R. So I = V ÷ R and R = V ÷ I. Example: 12 V across a 4 Ω resistor gives 3 A.
Key takeaway: V = IR.Series: add them, R = R1 + R2 + … Parallel: 1/R = 1/R1 + 1/R2 + …; for two resistors R = R1R2 ÷ (R1 + R2). 6 Ω and 3 Ω give 9 Ω in series and 2 Ω in parallel.
Key takeaway: series adds; parallel is always less than the smallest.A path with almost no resistance, for example a wire straight across a battery. By I = V ÷ R the current becomes very large, the wires and battery heat up and can start a fire. Fuses and circuit breakers cut the current when this happens.
Key takeaway: tiny resistance, huge current, heat.Metals (copper, aluminum, iron, steel, silver, gold) and graphite are conductors. Plastic, rubber, glass, dry wood, paper, cotton and air are insulators. Water with salt or other dissolved substances in it conducts, which is why electricity and water are dangerous together.
Key takeaway: metals and graphite conduct; plastic, rubber and glass insulate.Conventional current is drawn from + to − around the outside circuit, the way a positive charge would move; this convention was chosen before the electron was discovered. In metal wires the moving charges are electrons, which are negative, so they actually drift from − to +. Both describe the same current.
Key takeaway: conventional current + to −; electrons − to +.An ammeter measures the current through a part, so the current must pass through it: it goes in series, in the loop. A voltmeter compares two points, so it goes across the part, in parallel. An ideal ammeter has zero resistance and an ideal voltmeter has infinite resistance, so neither changes the circuit.
Key takeaway: ammeter in series, voltmeter in parallel.