AC Power, Impedance, Transducers, Batteries by the Numbers, and Regulators
Unit 2: Fundamentals of Electricity and Electronics. Lesson 14 of 60 in CBET Academy.
The second set of electronics facts the exam draws on: how AC power is described and delivered, how reactance becomes impedance, what makes a component active, how batteries are specified, and how a switching regulator fails.
Power distribution in the United States
Generators produce AC at a few kilovolts; step-up transformers raise it to hundreds of kilovolts for transmission because losses fall as current falls; step-down transformers at substations and on poles bring it to 240 V for buildings. Homes and most hospital branch circuits use the split-phase system: two 120 V lines of opposite phase with a grounded neutral between them, giving 120 V line to neutral and 240 V line to line, at 60 Hz. The National Electrical Code is NFPA 70; the NESC (National Electrical Safety Code, from IEEE) covers utility transmission. Transformer math: V primary / V secondary = N primary / N secondary; stepping 240 V up to 6,000 V for a defibrillator charger needs a turns ratio of 240 / 6,000 = 0.04 (primary to secondary), that is 25 secondary turns per primary turn.
True, reactive, and apparent power
In AC circuits with inductors and capacitors, voltage and current fall out of phase. True (real) power P, in watts, does work. Reactive power Q, in VAR (volt-amperes reactive), shuttles back and forth without doing work. Apparent power S, in VA, is what the supply must deliver: S squared = P squared + Q squared, a right triangle with S as the hypotenuse. 180 W with 240 VAR gives S = square root of (180 squared + 240 squared) = 300 VA. Power factor is P / S, 0.6 here; UPS units and generators are rated in VA, so a low power factor means less usable wattage.
Reactance and complex impedance
An inductor's reactance is XL = 2 x pi x f x L; a capacitor's is XC = 1 / (2 x pi x f x C). A 40 mH inductor at 60 Hz: 2 x 3.1416 x 60 x 0.040 = 15 ohms. Impedance combines resistance and reactance as Z = R + jX, where the reactive part is the imaginary component, written with j (or i) to show it is 90 degrees out of phase; an ideal 30 mH inductor at 60 Hz has Z = 11.3j ohms with no real part, and a real coil with 0.01 ohm of wire resistance has Z = 0.01 + 11.3j. Inductance is in henries (usually millihenries), capacitance in farads (usually microfarads). Filters are named by what they pass: low-pass, high-pass, band-pass, band-stop (the notch filter is a narrow band-stop).
Passive, active, and transducers
Passive components (resistors, capacitors, inductors, the memristor) consume or store energy and cannot amplify. Active components (transistors, op-amps, ICs) need a power source and provide gain. A thermistor is passive; a transistor is active. A transducer converts one form of energy to another: a sensor turns pressure, temperature, light, or sound into an electrical signal; an actuator turns an electrical signal into motion, heat, light, or sound. A piezoelectric crystal is both: pressure makes charge, and charge makes it move, which is why one ultrasound element sends and receives.
Battery specifications
- Voltage per cell (chemistry sets it; a AA is one cell).
- Capacity in amp-hours or watt-hours.
- Energy density: energy per unit weight; it decides how heavy a battery a device must carry.
- Internal resistance: rises with age; limits current and causes sag under load.
- Shelf life: how well charge holds while unused; self-discharge rate.
- Discharge curve: how voltage falls over a discharge; a flat curve keeps a device happy until the end.
- Cycle life for rechargeables: the number of charge cycles before capacity falls.
- C-rate: charge or discharge current relative to capacity. A 60 kWh battery charged at 0.5 C draws 0.5 x 60 = 30 kW; 1 C would empty or fill it in one hour.
Regulators and how they fail
A linear regulator drops the excess voltage across a transistor and wastes it as heat: simple, quiet, inefficient. A switching regulator (switch-mode supply, SMPS) turns the input on and off rapidly and averages the result with an inductor and capacitor; the output is set by the on-to-off ratio (duty cycle): efficient, light, noisier. Failure signatures: a switching element shorted passes the full input voltage through (a high-voltage fault, and the downstream boards fail with it); a switching element stuck open gives zero output. Test a regulator by measuring its input and output pins against ground and comparing to the rated values; replace it with the same part number. A GFCI is not a regulator; it cuts power when the return current is smaller than the outgoing current.
AC Power, Impedance, Transducers, Batteries by the Numbers, and Regulators, explained slowly
The power grid to the circuit board
Follow the electricity from the plant to the op-amp. On the way it is transformed, split, described by three kinds of power, opposed by reactance, stored in batteries, and regulated by switching circuits. The exam takes one snapshot at each stage.
Distribution
stage voltage why generator a few kV practical to generate step-up transformer hundreds of kV high voltage means low current means low line loss step-down at stations tens of kV, then hundreds of V safe to distribute building service 240 V split-phase two 120 V legs opposite in phase, neutral grounded in the middle branch circuits 120 V (or 240 V line to line) at 60 Hz
Codes: NFPA 70 is the National Electrical Code (building wiring); IEEE's NESC covers utility lines; NFPA 99 covers health care facilities. Transformer ratio: V primary / V secondary = N primary / N secondary. To step 240 V up to 6,000 V, the ratio is 240 / 6,000 = 0.04 (primary to secondary), meaning 25 secondary turns for every primary turn.
Three powers, one triangle
S (apparent, VA)
/|
/ | Q (reactive, VAR)
/ |
/___|
P (true, W)
S squared = P squared + Q squared; power factor = P / S
180 W and 240 VAR: S = sqrt(32,400 + 57,600) = sqrt(90,000) = 300 VA; power factor 0.6Watts do work and make heat; VARs circulate in inductors and capacitors; VA is what the wires and the UPS must carry. A 1,000 VA UPS feeding a 0.6 power factor load delivers only 600 W.
Reactance to impedance
component reactance formula 60 Hz example behavior inductor XL = 2 pi f L 40 mH: 2 x 3.1416 x 60 x 0.04 = 15 ohms opposes change in current; blocks high frequency capacitor XC = 1 / (2 pi f C) 10 uF: 1 / (377 x 0.00001) = 265 ohms opposes change in voltage; blocks DC impedance Z = R + jX ideal 30 mH: 0 + 11.3j ohms j marks the 90-degree phase shift
Angular frequency omega = 2 pi f = 377 rad/s at 60 Hz. Inductance is in henries (mH in practice); capacitance in farads (uF in practice). Filters by what they pass: low-pass, high-pass, band-pass, band-stop (a notch is a narrow band-stop).
Passive, active, transducer
passive resistor, capacitor, inductor, memristor, thermistor no gain; may store energy active transistor, op-amp, IC, SCR needs supply; provides gain or control sensor pressure, temperature, light, sound -> electrical the input side of every monitor actuator electrical -> motion, heat, light, sound pumps, heaters, displays, speakers
The piezoelectric crystal is the exam's favorite two-way transducer: squeeze it and it makes charge (sensor), charge it and it moves (actuator). Photoluminescence (light from radiation) and the pyroelectric effect (voltage from heating) are the distractors.
Battery datasheet
specification meaning why it matters voltage per cell set by chemistry cells in series reach the working voltage capacity Ah or Wh runtime energy density energy per kilogram decides the weight of the pack internal resistance ohms inside the cell; rises with age sag under load; heat shelf life charge retained while unused spares on the shelf discharge curve voltage versus state of charge flat curve keeps electronics happy cycle life charges before capacity drops replacement schedule C-rate current relative to capacity (1 C empties in 1 h) 60 kWh at 0.5 C charges at 30 kW
Regulators
type how traits failure signature linear transistor drops the excess as heat simple, quiet, inefficient runs hot; drifts switching chops input on and off, filters the average efficient, light, noisy switch shorted: full input passes through; switch open: zero output
Test: measure the regulator's input and output pins against ground and compare with the rating. A GFCI, by contrast, is a safety device that opens the circuit when return current falls short of outgoing current.
How the exam asks it
- "Which system sends 120 V across two lines in opposite phase with a central earth line?" Split-phase.
- "Winding ratio to step 240 V to 6,000 V?" 0.04.
- "Apparent power from 180 W and 240 VAR?" 300 VA.
- "Reactance of 40 mH at 60 Hz?" About 15 ohms. "Impedance of an ideal 30 mH inductor at 60 Hz?" 11.31j ohms.
- "Which is an active component: capacitor, inductor, thermistor, transistor?" Transistor.
- "Which battery characteristic most affects weight?" Energy density.
- "Rapid on-off signals to provide consistent power?" A switching power supply.
What to memorize
- Step-up to transmit, step-down to use; split-phase 120/240 at 60 Hz; NEC is NFPA 70; NESC is IEEE.
- S squared = P squared + Q squared; W, VAR, VA; power factor.
- XL = 2 pi f L; XC = 1 / (2 pi f C); Z = R + jX; henries, farads.
- Passive versus active; sensor versus actuator; piezoelectric both.
- Battery specs by name; C-rate times capacity.
- Switching regulator duty cycle; shorted gives full input, open gives nothing.