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

## Why it matters

Transformers are everywhere in power systems: the pole or pad-mount transformer outside a building, the control transformer inside a machine's panel that turns 480 V into 120 V or 24 V, the doorbell transformer, and the isolation transformers used on test benches. Electricians size and connect them, maintenance mechanics replace control transformers and fuses, and engineers choose ratings. All of that starts with one idea, the **turns ratio**.

## How a transformer works

A transformer has two (or more) coils of wire wound on a shared iron core:

- The **primary** winding is connected to the source.
- The **secondary** winding is connected to the load.

AC current in the primary creates a changing magnetic field in the core. That changing field passes through the secondary and **induces** a voltage in it (Faraday's law of induction). There is no electrical connection between the windings, only a magnetic one, which is why transformers also provide **isolation**.

Because induction needs a **changing** field, a transformer does not work on steady DC. Connect a transformer primary to DC and it acts almost like a short circuit of wire resistance: it overheats. This is one reason AC became the standard for power grids: transformers make it easy to step voltage up for transmission (less current, so less loss in the lines) and down for use.

## The turns ratio

For an ideal transformer, the voltage per turn is the same on both windings:

```text
Vs / Vp = Ns / Np
Vs = Vp × Ns / Np
```

where Np and Ns are the number of turns on the primary and secondary.

- **Step-down:** fewer secondary turns, lower secondary voltage.
- **Step-up:** more secondary turns, higher secondary voltage.

## Currents: power in equals power out

An ideal transformer has no losses, so apparent power is the same on both sides:

```text
Vp × Ip = Vs × Is
Is / Ip = Np / Ns
```

**Stepping voltage down steps current up** by the same ratio, and vice versa.

## Worked examples

**Example 1: a control transformer.** A 480 V primary with 2,000 turns and a secondary with 500 turns.

```text
Turns ratio Np : Ns = 2,000 : 500 = 4 : 1
Vs = 480 × 500 / 2,000 = 120 V
```

If the 120 V control circuit draws 2 A:

```text
Ip = Is × Ns / Np = 2 × 500 / 2,000 = 0.5 A
Check: 480 × 0.5 = 240 VA = 120 × 2 ✓
```

**Example 2: sizing by VA.** A 24 V secondary must supply a load of 1.5 A. The transformer's VA rating must be at least `24 × 1.5 = 36 VA`; a designer would choose a 40 VA or 50 VA unit for margin and inrush current.

**Example 3: step-up.** A 12 V primary, 100 turns, and a secondary of 1,000 turns.

```text
Vs = 12 × 1,000 / 100 = 120 V
```

(This is the principle of an inverter's output stage, not something to build.)

## Real transformers

- **Efficiency** is high (often 95–99% for power transformers), but there are copper losses (I²R heating in the windings) and core losses (eddy currents and hysteresis in the iron).
- **Regulation:** secondary voltage sags slightly as load increases.
- **Nameplates** show kVA, primary and secondary voltages, frequency, impedance (%Z) and connection diagrams. Many control transformers have multiple primary taps, such as 240/480 V, selected by jumpers.
- **Three-phase transformers** are connected delta or wye on each side; you will study connections and code requirements in the electrical code and installations course.

## Common mistakes

- **Inverting the ratio.** Always ask: is this step-up or step-down? The answer should match.
- **Forgetting the current goes the other way.** Lower voltage means higher current on that side, so conductors and fuses on the low side are often larger.
- **Using transformers on DC.**
- **Ignoring the VA rating.** Overloading causes overheating and shortens the insulation's life.

## Safety and real-world requirements

Transformers can deliver very high fault currents on their secondaries, and some can back-feed a "dead" circuit to a dangerous voltage. Connecting, testing or replacing a transformer is done only after employer training, under lockout/tagout procedures (https://www.osha.gov/control-hazardous-energy) and an electrical safety program based on NFPA 70E (https://www.nfpa.org/codes-and-standards/nfpa-70e-standard-development/70e), and installation work requires a licensed electrician. Checked on 2026-10-23.

## Recap

- AC in the primary makes a changing magnetic field that induces voltage in the secondary.
- `Vs = Vp × Ns / Np`; current scales the opposite way: `Is = Ip × Np / Ns`.
- VA in ≈ VA out; size transformers by VA with margin.

## Try it

Open the **Do** tab and write the secondary-voltage formula in a transformer calculator.


Use the turns ratio to compute transformer secondary voltage, primary and secondary current, and a VA rating.

Transformers

Transformers Explained - How transformers work

Transformer Basics - Introduction to Ratios and Calculations

## Why it matters

Motors turn most of the world's industrial electricity into motion: pumps, fans, conveyors, compressors and machine tools. Industrial machinery mechanics replace and align them, electricians wire and protect them, and engineers select them. Knowing how the two big families, **DC motors** and **AC induction motors**, work explains their nameplates, why their speeds behave the way they do and what usually goes wrong.

## The principle

A current-carrying conductor in a magnetic field feels a force. Bend the conductor into a loop on a shaft, and the forces on its two sides make a **torque** that turns the shaft. Every electric motor is a way of keeping that torque pointing the same way as the shaft rotates.

Two main parts:

- **Stator:** the stationary part (frame, magnets or field windings).
- **Rotor** (in DC machines often called the **armature**): the rotating part on the shaft.

## DC motors

In a **brushed DC motor**, the rotor carries the windings. A **commutator** (a segmented copper ring) and carbon **brushes** reverse the current in each rotor coil every half-turn, so the torque keeps the same direction.

- **Speed** rises with applied voltage. Lower the voltage and the motor slows; that makes speed control simple.
- **Direction** reverses when you reverse the polarity of the supply (for a permanent-magnet motor).
- **Torque** rises with current. At stall (rotor held still) the current is limited only by winding resistance, so stall current is high and windings overheat quickly.
- **Wear:** brushes and commutators wear and spark, so brushed motors need maintenance.

**Brushless DC (BLDC)** motors put permanent magnets on the rotor and use electronics to switch the stator coils. They are efficient and low-maintenance, and are found in drones, computer fans, power tools and electric vehicles.

DC motors also appear in older industrial drives (steel mills, cranes, elevators), many of which have been replaced by AC drives.

## AC induction motors

The **three-phase induction motor** is the workhorse of industry: rugged, cheap and almost maintenance-free.

- The three stator windings, fed by three-phase AC 120° apart, create a **rotating magnetic field**.
- The rotor is usually a **squirrel cage**: aluminium or copper bars shorted together by end rings. There is no electrical connection to it.
- The rotating field sweeps past the bars and **induces** current in them (like a transformer secondary). Those currents, in the field, produce torque.

**Synchronous speed** is the speed of the rotating field:

```text
Ns (rpm) = 120 × f / P
```

where f is the supply frequency and P the number of poles. At 60 Hz, a 4-pole motor's field turns at 120 × 60 / 4 = 1,800 rpm.

The rotor always turns a little slower than the field; otherwise the bars would see no change in field and no current would be induced. The difference is **slip**:

```text
slip = (Ns − N) / Ns
```

A 4-pole, 60 Hz motor with a nameplate speed of 1,750 rpm has a slip of 50 / 1,800 ≈ 2.8%.

- **Direction:** swapping any two of the three supply phases reverses the rotation.
- **Starting current** (inrush) is often 5–8 times the running current, which is why motor circuits use time-delay protection, and why larger motors use soft starters or **variable-frequency drives (VFDs)**.
- **Speed control:** because speed depends on frequency, a VFD changes the frequency to change the speed.
- **Single-phase induction motors** (in homes) need a start winding, often with a capacitor, because a single-phase field pulses instead of rotating.

## Comparing them

| | Brushed DC | AC induction (3-phase) |
|---|---|---|
| Speed control | Change voltage | Change frequency (VFD) |
| Reversing | Swap DC polarity | Swap two phases |
| Maintenance | Brushes, commutator | Mainly bearings |
| Typical use | Small tools, toys, automotive, legacy drives | Pumps, fans, conveyors, compressors |

## Common failures (awareness)

- **Bearings** wear from misalignment, belt over-tension or poor lubrication: noise, heat, vibration.
- **Winding insulation** breaks down from overheating, moisture or voltage spikes; tested with an insulation resistance tester by trained staff.
- **Single phasing:** a three-phase motor losing one phase draws high current and overheats if protection does not trip.
- **Brush wear** in DC motors.

## Safety and real-world requirements

Motors start automatically, store rotating energy and are supplied at high voltage. Inspection or repair requires the machine to be isolated and locked out under the employer's lockout/tagout program (https://www.osha.gov/control-hazardous-energy), and electrical work on motor circuits is done by trained, qualified people following NFPA 70E (https://www.nfpa.org/codes-and-standards/nfpa-70e-standard-development/70e). Checked on 2026-10-23. A small battery-powered DC toy motor is the only motor to experiment with at home.

## Recap

- Motors make torque from current in a magnetic field.
- DC: commutator and brushes; speed follows voltage; reverse by polarity.
- Induction: rotating field from three-phase AC; `Ns = 120f / P`; slip makes torque; reverse by swapping two phases; VFDs control speed.

## Try it

Take the quiz in the **Do** tab.


Compare how DC motors and AC induction motors work, how their speed is controlled and how they fail.

Motors

How does an Electric Motor work?  (DC Motor)

How Electric Motors Work - 3 phase AC induction motors  ac motor

Build or load a series circuit with at least five test points: battery, switch (or a removable jumper), resistor, LED, return wire. Draw its schematic and number the test points.

Write the expected voltage at each test point (measured from the battery's − terminal) before any fault is planted, using Ohm's law and KVL.

Have a fault planted without watching. Write down the symptom in one sentence.

List three hypotheses, most likely first, and the single measurement that would test each.

Half-split: measure at the middle test point first, then keep halving. Record every reading in a table before deciding the next test.

When the readings point to one part, disconnect the battery (or stop the simulation) and confirm with a resistance or continuity test.

Fix the fault, reconnect and verify that every test point matches your expected values.

Repeat with two more faults, then write a short report for each: symptom, tests and readings, cause, fix, verification.

## Why it matters

Troubleshooting is where electrical knowledge earns its keep. Maintenance mechanics and electricians are judged on how quickly and safely they find faults; engineers debug prototypes; physicists debug experiments. The difference between a beginner and an experienced troubleshooter is rarely knowing more facts. It is following a **systematic test plan** instead of swapping parts at random.

## Three kinds of fault

- **Open circuit:** a break in the path (a broken wire, blown fuse, loose terminal, failed switch contact). Current stops in that path. Across the open, you measure the full supply voltage; resistance reads `OL`.
- **Short circuit:** an unintended low-resistance path (damaged insulation, a solder bridge, a wire strand touching the wrong terminal). Current rises sharply; fuses or breakers should open. Voltage across the shorted part reads near zero.
- **High-resistance connection:** a corroded or loose joint that still conducts but drops voltage and heats up. Loads run weakly or intermittently.

A **ground fault** is a short from a conductor to the equipment frame or earth; protective devices such as GFCIs detect them.

## A systematic method

1. **Gather information.** What should it do? What does it do now? When did it change? What was last worked on? Read the schematic.
2. **Observe safely.** Look, listen and smell (scorch marks, loose wires, hot parts) without touching anything energized.
3. **Form hypotheses.** List possible causes, most likely and easiest to check first.
4. **Test, one variable at a time.** Make a measurement that splits the possibilities. Write down every reading.
5. **Fix the cause**, not just the symptom (a fuse that blew because of a short will blow again).
6. **Verify** that the whole system works, then **document** what you found and did.

## Half-splitting

In a long series path, testing every point in order is slow. **Half-splitting** tests the middle first: if voltage is correct there, the fault is downstream; if not, it is upstream. Each test halves the search space, so a path with 16 test points needs at most 4 tests.

**Worked example.** A battery circuit: 9 V battery → switch → fuse → resistor R1 → LED → back to battery. The LED is dark. Measuring voltage from the battery's − terminal (as common) at each point:

```text
After switch:         9.0 V   (good so far)
After fuse:           9.0 V
After R1 (LED anode): 9.0 V   ← no drop across R1, so no current is flowing
At the LED cathode:   0 V
```

With no current, there is no drop across R1, so the full 9 V appears right up to the LED and nothing appears after it. **The open is in the LED or its connections.** Disconnect the battery and check the LED: it is in backwards. Reverse it, retest: the LED anode now reads about 2 V and the LED lights.

Compare with a short: if R1 were bypassed by a stray wire, the LED would flash and die, and the voltage across R1 would read 0 V while current was high.

## Voltage-drop and resistance tests

- **Voltage-drop testing** (on a powered, safe, low-voltage circuit): a good closed switch or wire should drop almost nothing; a noticeable drop across a connection points to high resistance.
- **Resistance and continuity testing** (power off, isolated): confirms opens and shorts in individual parts.

On real installations, both are done only by qualified people, after verifying the absence of voltage before resistance tests.

## Common mistakes

- **Swapping parts without testing.** It is expensive and often misses the real cause.
- **Not recording readings.** You lose track of what you have ruled out.
- **Changing two things at once.** You will not know which one fixed it.
- **Forgetting the obvious.** Is it switched on? Is the battery charged? Is the fuse the right type?
- **Not finding the root cause** of a blown fuse or tripped breaker.

## Safety and real-world requirements

Most industrial troubleshooting is done with equipment de-energized and locked out (https://www.osha.gov/control-hazardous-energy). Energized testing is allowed only when justified, by qualified persons with the right PPE and procedures under NFPA 70E (https://www.nfpa.org/codes-and-standards/nfpa-70e-standard-development/70e). Electricians work toward this through a registered apprenticeship (https://www.apprenticeship.gov) and a state or local licence; your state's licensing board sets the rules. Engineers who sign off designs may need a PE licence (https://ncees.org). Checked on 2026-10-23. Practise only on battery circuits and simulators until you have that training.

## Recap

- Faults are opens, shorts or high-resistance connections.
- Gather, observe, hypothesise, test one thing at a time, fix the cause, verify and document.
- Half-split long paths; read the voltage pattern to locate an open.

## Try it

Open the **Do** tab and find planted faults in a simulator or a battery circuit with a written test plan.


Find opens, shorts and high-resistance faults with a systematic, written test plan.

Troubleshooting circuits

Industrial Electrical Troubleshooting Made Simple

Electrical Troubleshooting Basics

Transformer turns ratios, how DC and AC induction motors work, and a systematic method for finding circuit faults.