Learn DC and AC circuit analysis, power factor and three-phase basics, safe measurement on battery circuits, simulation, transformers, motors and systematic troubleshooting.

Electrical Circuits

Set up a results table on paper: measurement, dial setting, jack used, expected value, measured value.

Put the black lead in COM and the red lead in VΩ. Set the dial to DC volts and measure one AA cell, then the pair (or the 9 V battery). Record the readings and note what happens when you swap the probes.

Disconnect everything from the resistor. Set the dial to Ω and measure the 1 kΩ resistor, holding the leads (not the metal tips). Check it is within its tolerance band.

Set the dial to continuity. Touch the probes together (it should beep), then test a jumper wire end to end, then the resistor. Write down which beep and why.

Calculate the current you expect from your battery voltage and the measured resistance (I = V / R). Write it in mA.

Disconnect the battery. Move the red lead to the mA jack and set the dial to DC mA. Build the loop battery → resistor → meter → back to battery, so the meter is in series. Reconnect and record the current.

Disconnect the battery, then move the red lead back to VΩ and set the dial to DC volts. Say out loud why this step matters.

Compare your measured current with your calculation and write one sentence on any difference (battery voltage under load, resistor tolerance, meter resistance).

## Why it matters

A multimeter is the most-used test instrument in electrical work. Electricians use it to verify a circuit is dead before touching it, maintenance mechanics use it to check motor windings and control circuits, and engineers and physicists use it on every prototype. Using one correctly is a safety skill as much as a measurement skill: the wrong setting or lead position can blow the meter's fuse or, on high-energy circuits, cause an arc flash. Here you learn the habits on batteries, where mistakes are cheap.

## Parts of a digital multimeter

- **Display:** shows the reading, its unit and symbols such as `−` (reversed polarity) or `OL` (over limit, the value is too high for the range or the circuit is open).
- **Rotary dial:** selects what to measure: `V⎓` or `DCV` (DC volts), `V~` or `ACV` (AC volts), `Ω` (resistance), a sound-wave or diode symbol (continuity/diode test), `A` or `mA` (current).
- **Jacks:** `COM` (common, black lead) is always used. `VΩ` (red lead) for voltage, resistance and continuity. `mA` or `A` (red lead) only for measuring current. The current jacks are fused.
- **Auto-ranging** meters choose the range themselves. On a manual-ranging meter, start on a range above what you expect and step down.

## Measuring voltage (in parallel)

Voltage is measured **across** a component or source: put the probes on the two points, in parallel with what you are measuring. The circuit stays as it is.

**Example:** a fresh AA cell reads about 1.5–1.6 V; a used one might read 1.2 V. A 9 V battery reads about 9.0–9.6 V when new. If the display shows `−1.55`, the leads are reversed; the reading is still right.

## Measuring resistance (power off)

Resistance is measured with the meter's own small battery, so **the component must be unpowered**, and ideally removed from the circuit so other parts in parallel do not change the reading.

**Example:** a resistor with bands brown-black-red-gold is 1 kΩ ±5%, so expect 950–1,050 Ω. If you hold both probe tips with your fingers, your body's resistance (often hundreds of kilohms) is in parallel and the reading drops: hold the leads, not the tips.

## Continuity

The continuity setting beeps when the resistance between the probes is very low, usually under about 30–50 Ω. It answers "is this wire, fuse or switch contact connected?". Again, only on unpowered parts.

## Measuring current (in series)

Current is measured **through** the circuit, so the meter must become part of the path:

1. Turn the circuit off (disconnect the battery).
2. Move the red lead to the `mA` jack and set the dial to `mA` DC.
3. Break the circuit at one point and connect the meter across the gap, so all the current flows through the meter.
4. Reconnect the battery and read.
5. **Afterwards, move the red lead back to `VΩ`.**

The meter in current mode is almost a short circuit. If you leave the lead in the mA jack and then try to "measure the voltage" of a battery, you short the battery through the meter and blow its fuse. On a high-energy circuit the same mistake can cause an arc flash. This is the single most common multimeter error.

**Example:** two AA cells (3 V) in series with a 1 kΩ resistor should read about 3 mA, which matches Ohm's law: 3 V / 1,000 Ω = 0.003 A.

## Meter ratings and real-world practice

Meters used on building and industrial systems carry an overvoltage **category (CAT II, III or IV)** and a voltage rating, and their leads must match. Professionals use a **test-before-touch** routine: test the meter on a known live source, test the circuit, then test the meter again on the known source. That routine, voltage testing on energized equipment and choosing protective equipment are covered by an employer's electrical safety program based on NFPA 70E (https://www.nfpa.org/codes-and-standards/nfpa-70e-standard-development/70e) and OSHA electrical rules (https://www.osha.gov/electrical). You may only do them after that training and under supervision. Checked on 2026-10-23.

The videos for this lesson include measurements on wall outlets and car systems by experienced people. Watch them for technique only. **Do not copy those measurements at home.**

## Common mistakes

- **Leaving the red lead in the mA or A jack.** Check the jacks every time you change the dial.
- **Measuring resistance on a powered circuit.** It gives nonsense and can damage the meter.
- **Measuring current in parallel.** Current is always measured in series.
- **Reading the wrong unit.** 1.00 on the kΩ range is 1,000 Ω.
- **Using a cheap, unrated meter on high-energy circuits.** Never do this; at home, use batteries only.

## Recap

- Voltage: in parallel, red in `VΩ`. Resistance and continuity: power off. Current: in series, red in `mA`, then move it back.
- `OL` means over range or open circuit.
- Real installations need a rated meter, training, supervision and test-before-touch.

## Try it

Open the **Do** tab and practise all four measurements on batteries and a resistor.


Measure voltage, resistance, continuity and current safely on battery-powered circuits.

Using a multimeter

How to Use a Multimeter for Beginners - How to Measure Voltage, Resistance, Continuity and Amps

How to use a multimeter like a pro! The Ultimate guide

Measure your battery voltage and write it down. Using Vf = 2.0 V and a target of 10 mA, calculate the resistor value and pick the next standard value up.

With the battery disconnected, use continuity mode to confirm which holes are connected: one five-hole row, and one power rail end to end.

Place the resistor from the + rail to an empty row, the LED's long leg (anode) in that row and its short leg in a new row, and a jumper from that row to the − rail.

Draw the circuit as a schematic (battery, resistor, LED) next to a sketch of the breadboard layout, and check the two match.

Connect the battery. If the LED does not light, disconnect, then check polarity, rows and the battery using the troubleshooting list in the reading.

Measure the voltage across the LED and across the resistor. Check that they add up to the battery voltage (within a few percent).

Calculate the current from the resistor voltage (I = V_R / R). Compare it with your 10 mA target.

Disconnect the battery and store the parts. If you used a 9 V battery, cover its terminals or put it back in its packaging.

## Why it matters

A **breadboard** lets you build and change a circuit without soldering. Engineers prototype on them, physics labs use them for experiments, and trade schools use them to teach how series and parallel connections look in real life. Building an LED circuit is the classic first build because it combines Ohm's law, polarity and measurement in one small, safe project.

## How a breadboard is connected inside

Under the plastic, metal clips join groups of holes:

- **Terminal strips:** in the main area, each short row of five holes (often labelled a–e and f–j) is connected. The two halves are separated by a centre channel, so a–e is not connected to f–j.
- **Power rails:** the long lines along each edge, usually marked red (+) and blue or black (−), are connected along their length. On some full-size boards the rails are split in the middle; check with your meter's continuity setting.

Two component legs in the **same five-hole row** are connected. Legs in different rows are not, unless a wire joins them.

## The LED

A **light-emitting diode (LED)** lets current flow in one direction only and glows when it does.

- The **anode** (+) is the longer leg; the **cathode** (−) is the shorter leg, often next to a flat edge on the rim.
- An LED has a roughly fixed **forward voltage (Vf)** when lit: about 1.8–2.2 V for red, yellow and green, about 3.0–3.3 V for blue and white.
- An LED does **not** limit its own current. Connected straight to a battery, it draws too much current and burns out. Always use a series resistor.

## Sizing the resistor

The resistor takes the voltage the LED does not use:

```text
R = (Vsupply − Vf) / I
```

Typical small LEDs are happy at 5–15 mA (check your LED's datasheet; 20 mA is often the maximum).

**Example 1: two AA cells (3.0 V), red LED (Vf ≈ 2.0 V), target 10 mA.**

```text
R = (3.0 − 2.0) / 0.010 = 100 Ω
```

**Example 2: 9 V battery, red LED, target 15 mA.**

```text
R = (9 − 2.0) / 0.015 = 467 Ω  → use the next standard value up, 470 Ω
Resistor power = I² × R = 0.015² × 470 = 0.106 W  (a 0.25 W resistor is fine)
```

Choosing the next value **up** keeps the current a little lower, which is the safe direction.

## Building the circuit

1. Battery holder + to the red rail, − to the blue rail (connect the battery last).
2. Resistor from the red rail to an empty row, say row 10.
3. LED anode (long leg) in row 10; cathode in row 12.
4. A jumper wire from row 12 to the blue rail.
5. Connect the battery. The LED should light.

Electrically this is a simple series loop: battery → resistor → LED → back to battery.

## Measuring it

- **Voltage across the LED:** red probe on the anode row, black on the cathode row. Expect about 2 V for red.
- **Voltage across the resistor:** expect the remainder, for example 3.0 − 2.0 = 1.0 V.
- **KVL check:** the two drops should add up to the battery voltage measured under load.
- **Current:** either measure in series (break the loop at the jumper and insert the meter in mA mode) or calculate it from the resistor's voltage: `I = V_R / R`. The second way is safer for the meter and usually accurate enough.

## Troubleshooting a dark LED

- LED backwards? Swap its legs (a reversed LED at these voltages just stays dark).
- Both legs in the same row? Then the LED is shorted out.
- Resistor and LED not sharing a row? Use your meter's continuity mode to check the path.
- Battery flat or rail split? Measure the voltage at the rails.

## Common mistakes

- **No resistor.** The LED flashes brightly and dies.
- **Placing a part across the centre channel the wrong way.** Components that must connect need a shared row.
- **Assuming the rails run the whole length.** Check for a split.
- **Leaving the battery connected while rebuilding.** Disconnect it before moving parts.

## Safety

This lesson uses 3 V or 9 V batteries only. Never use a wall adapter you have opened, a mains supply or a lithium-ion pack for these builds. Lab bench power supplies are used only in a school or workplace lab with your instructor.

## Recap

- Rows of five are connected; rails run along the edges; the centre channel separates the halves.
- LEDs have polarity and a forward voltage; they always need a series resistor: `R = (Vs − Vf) / I`.
- Measure the drops and check that they add up to the supply.

## Try it

Open the **Do** tab and build and measure your LED circuit, or build it in a simulator if you have no parts yet.


Size a resistor for an LED, build the circuit on a breadboard and check it with your meter.

Breadboard circuits

Breadboard tutorial: How to use a breadboard (for beginners)

Easy LED Circuit Tutorial // Becky Stern

Open the simulator, choose File → New Blank Circuit, and add a 10 V DC source.

Build the series-parallel circuit from the series and parallel lesson: R1 = 40 Ω in series with R2 = 60 Ω in parallel with R3 = 30 Ω. Set each value by double-clicking the part.

Hover over each resistor and record its voltage and current. Compare them with the worked example and fix any wiring mistakes.

Make a fault: delete the wire to R3 (an open circuit). Record what happens to the total current and to the voltage across R1, and explain why.

Make another fault: put a plain wire across R2 and R3 (a short). Record the total current and the power in R1, and note which part would overheat in real life.

Start a new blank circuit and build the two-loop circuit from the Kirchhoff lesson (12 V, 6 V, 2 Ω, 4 Ω, 6 Ω). Check that R3 carries about 1.36 A.

Replace the 6 V source with an AC source (60 Hz) feeding a resistor and a 10 µF capacitor in series. Right-click the capacitor → View in Scope and note whether current leads or lags voltage.

Export or screenshot your circuits (File → Export As Link or a screenshot) and save them with your notes.

## Why it matters

Simulators let you build any circuit, at any voltage, and watch current flow without risk or cost. Engineers simulate designs before building them, technicians use simulators to understand a fault before opening a panel, and teachers use them to show what a meter would read. A free browser simulator is the safest place to try the things you must never try on real equipment, such as what a short circuit does to current.

## Two free tools

- **Falstad Circuit Simulator** (https://www.falstad.com/circuit/) runs in your browser with no account. It animates current as moving dots and colours wires by voltage, which makes KVL and KCL visible. It includes resistors, capacitors, inductors, AC sources, diodes, transistors, transformers and logic gates, and has dozens of built-in example circuits under the **Circuits** menu.
- **Tinkercad Circuits** (https://www.tinkercad.com/circuits) from Autodesk needs a free account. It looks like a real workbench, with breadboards, batteries, LEDs, multimeters and even an Arduino, so it is ideal for rehearsing a physical build.

Engineers also use **SPICE** simulators such as LTspice (free from Analog Devices). SPICE is more accurate for detailed electronics design, but it has a steeper learning curve; the habits you learn here carry over.

## Getting started in Falstad

1. Open the simulator. It loads an example (an LRC circuit). Choose **File → New Blank Circuit** to start clean.
2. Add parts from the **Draw** menu, or right-click the canvas. Common shortcuts: `r` resistor, `v` voltage source, `w` wire, `c` capacitor, `l` inductor.
3. Drag from one point to another to place a part. Ends that land on the same point are connected (a small dot shows a joint).
4. **Double-click** a part (or right-click → Edit) to change its value, for example 470 Ω or 9 V.
5. Hover over a part to see its voltage, current and power in the corner of the screen.
6. Use the **Reset** and **Run/Stop** buttons; the speed sliders on the right slow down or speed up the animation.

## Worked example: checking the series-parallel lesson

Rebuild example 3 from the series and parallel lesson: a 10 V source, R1 = 40 Ω, and R2 = 60 Ω in parallel with R3 = 30 Ω.

- Hover over R1: it should show about 166.7 mA and 6.67 V.
- Hover over R2 and R3: 55.6 mA and 111.1 mA, both at 3.33 V.

If the simulator disagrees with your hand calculation, one of them is wrong. Usually it is a wire that does not connect where you think it does.

## What simulators are good for

- **Checking hand calculations** for DC and AC circuits.
- **Trying "what if?" changes** quickly: double a resistor, add a branch, change the frequency.
- **Seeing AC behaviour:** add a scope trace (right-click a part → View in Scope) to see voltage and current waveforms and the phase shift in an inductor or capacitor.
- **Safely exploring faults:** an open wire, a shorted part, a failed component.

## Limits of simulation

- Parts are ideal unless you model otherwise: real batteries have internal resistance, real wires have resistance, and real LEDs vary.
- A simulator does not model fire, arc flash or shock. A circuit that "works" at 480 V in a simulator says nothing about whether it is safe to build.
- Simulators do not check codes. Wiring for buildings must follow the electrical code adopted locally (often based on NFPA 70, the National Electrical Code: https://www.nfpa.org/codes-and-standards/nfpa-70-standard-development/70) and is installed and inspected by licensed people. Checked on 2026-10-23.

## Common mistakes

- **Parts that look connected but are not.** Look for the joint dot, or drag a part slightly to see if the wire follows.
- **Forgetting a ground or return path.** Current needs a complete loop.
- **Wrong units.** In Falstad, type `4.7k` for 4.7 kΩ and `10u` for 10 µF.
- **Trusting the simulator blindly.** Always estimate the answer first.

## Recap

- Falstad: instant, no account, great for seeing current and voltage. Tinkercad: realistic workbench and breadboards.
- Hover to read values; double-click to edit; use the scope for AC.
- Simulators check your thinking; they do not make a real high-energy circuit safe.

## Try it

Open the **Do** tab and simulate two circuits from earlier lessons, then break them on purpose.


Build, measure and break circuits safely in a free browser simulator.

Circuit simulation

How to use the Falstad Circuit Simulator

LEDs & Breadboards With Arduino in Tinkercad

Using a multimeter safely, building and measuring a battery LED circuit on a breadboard, and simulating circuits in a free tool.