In 1819, Hans Christian Oersted held a compass near a wire and watched the needle twitch. That one twitch unfolds into everything below: three ways a current builds a magnetic field, two ways a field pushes back on current, and — at the end — the actual meters sitting inside every multimeter. Same idea, seven acts, one thread. Turn the dials.
Look straight down the wire — it's just a dot. Around that dot, the field curls in perfect circles: tighter and stronger close in, looser and weaker farther out. Point your right thumb along the current and your fingers curl the way the field points.
Now bend that same wire into a ring and see what its swirl adds up to.
Every point on the loop is still just wrapping the field around itself — but now all those little swirls stack through the center and add up into one straight bundle of field lines. One face becomes a north pole, the other a south. Stack N turns and the effect multiplies N times over.
One ring makes a weak little magnet. Line up dozens of rings in a row, and…
Pack the loops close together into a coil (a solenoid) and their individual bundles merge into one strong, uniform field running straight down the middle — exactly like a bar magnet, with a true north and south end. Slide an iron core inside, and that same current suddenly produces a far stronger field: iron doesn't fight the field, it joins in.
So far, current has only been making fields. Flip the script: put that current-carrying wire inside someone else's field.
Drop a current-carrying wire into an external magnetic field and it feels a sideways shove — perpendicular to both the current and the field (Fleming's left hand: field on the pointer, current on the middle finger, force on the thumb). Line the wire up parallel to the field and the shove disappears entirely.
One wire feels the push of an outside field. But every wire makes its own field too — so what happens when two current-carrying wires face each other?
Each wire sits inside the other's field from Act 1, and each gets shoved by it exactly as in Act 4. Run the currents the same direction and the wires pull together; reverse one and they push apart. No magnets required — just two currents, doing to each other what Acts 1 and 4 already taught you.
Straighten that logic back out: instead of two straight wires, bend one wire into a rectangle and drop the whole loop into a field.
The two long sides of a rectangular coil each get shoved by the field (Act 4), in opposite directions — and opposite forces offset from each other is exactly a torque. The coil twists to line its face up with the field. This one idea — current loop + field = torque — is the entire mechanism inside a galvanometer, and every electric motor ever built.
Add a spring that resists that twist, and you can read the twist angle off a dial. That's not a metaphor — that's literally a galvanometer.
Everything below is the same coil-in-a-field from Act 6, with a control spring added to balance the torque. What changes at each step is only what's wired around it — and that's the difference between a galvanometer, an ammeter, a voltmeter, and an ohmmeter.
The spring pushes back with a torque proportional to the deflection angle. Balance point: BIAN = kθ — so the pointer's angle is directly proportional to the current. A galvanometer can only ever read up to its coil's own tiny safe current (here, 5 mA).
To read real-world currents (amps, not milliamps), give most of the current an easy detour: a tiny shunt resistor Rs in parallel with the coil. Almost all the current sneaks through the shunt; only the safe sliver reaches the coil.
To read a voltage instead, do the opposite: add a big multiplier resistor Rm in series, so the combination draws only a hair of current and barely disturbs the circuit it's measuring.
Wire a fixed battery and a fixed internal resistance in series with the unknown resistor Rx, then read the current instead — and calibrate the dial directly in ohms. Short the terminals (Rx=0) and current is maximum: full-scale deflection. The higher Rx climbs, the less current flows, so the scale reads backwards — and, because I = V/(R+Rx) isn't linear in Rx, the tick marks bunch up on one side exactly like the real instrument.
Wire all four modes behind one selector switch and read a pointer instead of numbers, and you've built the analog multimeter sitting in a drawer somewhere. Swap the pointer for an LCD and you've built the digital one.