Chapter 2 · Electric current: the loop, the push and the limit
Circuits, voltage and Ohm's law
The first battery
The scene shows a battery, two wires and a bulb joined in a ring. The bulb lights only while the ring is closed; cut one wire and it goes dark. In 1800 Alessandro Volta described his pile: discs of zinc and copper separated by cloth soaked in brine, stacked in a column. It was the first steady source of current. Chemical reactions inside a battery separate charge and keep pushing it round the loop. A modern AA cell does the same at 1.5 V. Home experiments belong with small batteries only; the wall socket is another matter and can kill.
Current and voltage
Watch the dots drifting through the wire. Current, I, counts how much charge passes a point each second: I = Q / t. Its unit, the ampere, is one coulomb per second. If 0.5 A flows for 20 s, then Q = 0.5 × 20 = 10 C has passed. Voltage, V, is the push, the energy given to each coulomb: 1 V = 1 J/C, so a 1.5 V cell gives each coulomb 1.5 J. Think of water in pipes, with current as the flow and voltage as the pressure. The electrons drift well under a millimetre per second, yet the push travels round the loop almost at once.
Resistance and Ohm's law
Every material resists the flow a little, and resistance is measured in ohms. In 1827 Georg Ohm published the relation V = I·R, where V is the voltage in volts, I the current in amperes and R the resistance in ohms. Rearranged, I = V / R: for the same push, more resistance means less current. A 6 V battery across a 12 Ω resistor drives 6 / 12 = 0.5 A. A 9 V battery across 450 Ω gives 9 / 450 = 0.02 A, or 20 mA. In the scene the dots slow and crowd as you raise R; the sandbox does the sums for you.
Series: one road
Two identical 6 Ω bulbs share a 6 V battery. Joined in series, the current has one road, so resistances add: R = R₁ + R₂ = 12 Ω. Then I = 6 / 12 = 0.5 A flows through both, and each bulb takes half of the push: 0.5 × 6 = 3 V. Both glow dimly. Unscrew one bulb and the ring breaks, so both go out, which is why old strings of festive lights used to fail all at once.
Parallel: two roads
Now each bulb sits on its own branch straight across the battery, so each gets the full 6 V. The branches share the current: 6 / 6 = 1 A in each, 2 A from the battery in total. The combined resistance follows 1/R = 1/R₁ + 1/R₂ = 1/6 + 1/6, so R = 3 Ω, and the check works: 6 / 3 = 2 A. Adding a branch lowers the total resistance. Houses are wired in parallel, so every socket gets the full mains voltage and one dead lamp leaves the others lit.
Power and the fuse
Power is the rate of energy use: P = V·I, in watts. Compare the two layouts. In parallel, 6 V × 2 A = 12 W, bright. In series, 6 V × 0.5 A = 3 W, dim. With Ohm's law this is also P = I²R, the heat made in the wire. Too much current overheats a wire and can start a fire, so circuits are protected. A fuse is a thin strip that melts at its rated current, and a breaker flips open. A 16 A breaker on a 230 V circuit allows 230 × 16 = 3,680 W; plug in more and it trips. In the scene the fuse glows, then a gap opens.
In numbers
- 1800
- Volta describes his pile, the first steady battery
- V = I·R
- Ohm's law, published by Georg Ohm in 1827
- 3,680 W
- the limit of a 16 A breaker on a 230 V circuit