Robotics · Electronics basics · Grade 8

Measuring with a multimeter

The circuit does not light up. Where is the break? Find it not by eye but with a multimeter.

The situation

A circuit built at the club — a battery, two resistors, two LEDs — does not light up. The wires are in place, the resistors are new, the battery was bought yesterday… nothing can be seen by eye. Experts do not search in such cases — they measure: in a series circuit the break is where the whole voltage drops. Take the multimeter: measure voltage across the parts, measure current by breaking the circuit and connecting the meter in series, measure resistance and do the “continuity test” with the power off. The fault is random every time: a broken wire, a burnt-out resistor, a reversed LED, a flat battery, a poor contact or a short bridge. Can you find it in three measurements?

Topic

Measuring with a multimeter. The circuit does not work — where is the break? Voltage, current, resistance and the continuity mode

Key ideas

Voltage and current
Continuity
Finding the fault

Formulas

U = U_{1} + U_{2} + \dots + U_{n}

The rule of a series circuit: the source voltage is shared between the parts; in a circuit with no current every part has 0 V, and across the break there is the whole $U$ .

I = \frac{U - U_{L E D 1} - U_{L E D 2}}{R_{1} + R_{2}} = \frac{9 - 3.8}{320} \approx 16 mA

The current in a healthy circuit: ≈ 1.9 V across each of the two red LEDs, the rest across the resistors. The ammeter is connected in series, breaking the circuit.

U_{l o a d} = ℰ - I \cdot r

The battery voltage drops under load because of the internal resistance $r$ : a flat battery shows 7.5 V with no load, and 4.7 V in the circuit.

R_{c o n t a c t} = \frac{U_{c o n t a c t}}{I}

There cannot be a voltage between two legs in one column — if there is, there is a resistance between them: a cold solder joint or an oxidised contact.

Theory

Do not search — measure

Looking at a faulty circuit by eye helps little: a wire is broken inside its insulation, a resistor is whole on the outside, LED legs look alike. A multimeter shows what cannot be seen. The first question is always the same: is there current in the circuit? The LEDs are off — so either there is no current (a break), or the voltage is not enough (battery, poor contact), or an LED is connected wrongly.

Searching by voltage

In V⎓ mode the probes go in parallel across the two ends of a part. In a series circuit $U = U_{1} + U_{2} + \dots$ . If no current flows, the voltage across the resistors and LEDs is zero — almost the whole 9 V of the source drops across the break: on a broken wire, a burnt-out resistor or a reversed LED you will see 8–9 V (a volt or two “leak” through the LEDs into the multimeter’s own 10 MΩ). To find it faster, measure by halving the circuit: if there is 9 V from the battery “+” to the end of W₂, the fault is in that half, then halve it again. 7 parts can be checked in 3 measurements.

Continuity and the diode test

The multimeter’s “→| •)))” position sends its own 1 mA current and shows the voltage between the probes. If the wire is whole — 0.000 V and a beep (the “continuity test”); a broken wire — OL, silence. Applied to a diode or an LED: in the forward direction (red probe on the anode) ≈ 1.9 V, in reverse — OL. This is how a reversed LED is found: it shows 9 V and looks “broken”, but if you swap the probes you get 1.9 V. Important: these modes and Ω work only with the battery disconnected — the circuit’s current fools the meter.

Measuring current: in series, and the fuse

An ammeter is connected in series in the current path: take out a wire and put the probes in its place. The circuit is closed through the meter, the shunt resistance is small (1 Ω at 200 mA). Mistakes: in V mode in series — the circuit is “open” through 10 MΩ, the LEDs go out, the display shows 9 V; in A mode in parallel — the shunt short-circuits the battery and the 200 mA fuse blows. The mA jack is protected, the 10 A jack is unprotected but coarse: it shows 16 mA as 0.02 A. The rule: a large range first, then a smaller one — the display shows more digits.

The battery and the contacts

A flat battery plays tricks: with no load (disconnected from the circuit) it shows 7.5 V — “looks fine”. But its internal resistance has grown: when current flows in the circuit the voltage drops to $ℰ - I r$ — 4.7 V, and the LEDs are dim. That is why a battery is measured under load. A cold solder joint or an oxidised contact is an invisible resistor in the circuit: between two legs in one column there should be 0 V, and at the faulty place a few volts; in Ω mode (power off) 1.5 kΩ. A short bridge (a blob of solder or a strand of wire) bypasses the LED: the LED is off, it has 0 V across it, and the continuity test beeps.

About the model

The circuit is solved by the nodal method: every leg and wire end is a separate node, joined to the strip through a 0.01 Ω contact (a poor contact is 1.5 kΩ). LED: no current up to 1.9 V, then 2 Ω; in the diode test it shows ≈ 1.9 V at 1 mA (a real red LED has ≈ 1.7 V at this current). Battery: 9 V, 1.7 Ω; flat — 7.5 V, 1 kΩ. Multimeter: V⎓ 10 MΩ, A⎓ shunt (200 mA — 1 Ω, 20 mA — 10 Ω, 10 A — 0.01 Ω), 1999 counts, the mA jack fuse is 200 mA. Faults are chosen at random; a short bridge and a wire break are not visible in the picture — on purpose.

Did you know?

Most digital multimeters are “3½-digit”: the display shows 1999 at most — the first digit can be only 0 or 1. So measuring 2 V needs the 20 V range, while 1.999 V fits the 2000 mV range.
Cheap multimeters of the DT-830 type appeared in the 1980s and are still the world’s best-selling measuring instrument; inside is a single ICL7106 chip — an analogue-to-digital converter and display driver in one.

Inside the experiment

A real board in a hand-inked isometric drawing: turn it, place the parts, wire the circuit, write and upload the code — current and voltage are computed at once, and a wrong connection burns a part. Inside are missions, theory, a quiz and a guided tour.

More experiments in this section

Resistors: the colour code — Grade 7
Voltage divider and potentiometer — Grade 7
Capacitor: charging and the RC time — Grade 7
Diode and rectifier — Grade 8
The transistor — a switch — Grade 8