AC circuits and theory

NEETS Mod. 1 §3-1

NEETS Mod. 1 §3-1 — Ohm's law and electrical power Ohm's law is the foundation of all circuit calculation: the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance, expressed E = I × R, where E is electromotive force in volts, I is current in amperes, and R is resistance in ohms. Rearranged: I = E/R and R = E/I. If any two quantities are known the third is found. Resistance opposes current flow and depends on the conductor's material (resistivity), length (longer = more resistance), cross-sectional area (thicker = less resistance), and temperature (for metals, resistance rises with temperature). Electrical power — the rate of doing electrical work — is measured in watts: P = E × I. Combined with Ohm's law this gives the useful forms P =…

NEETS Mod. 2 §1-1

NEETS Mod. 2 §1-1 — AC vs DC, generation, and the sine wave Alternating current (AC) periodically reverses direction and continuously changes in amplitude, unlike direct current (DC) which flows in one direction at a steady value. AC is the shipboard standard for generation and distribution because its voltage is easily raised or lowered by transformers, allowing efficient transmission and simple motor design. AC is produced by electromagnetic induction: when a conductor loop rotates in a magnetic field, the induced voltage varies as the sine of the angle between the conductor's motion and the flux, tracing a sine wave. One complete positive-and-negative excursion is a cycle; the number of cycles per second is the frequency in hertz (Hz). Common shipboard frequencies are 60 Hz (US) and 50…

NEETS Mod. 2 §1-2

NEETS Mod. 2 §1-2 — Peak, RMS, average values and phase Because a sine wave is constantly changing, several values describe it. The effective, or root-mean-square (RMS), value is the most important: it is the DC value that would produce the same heating in a resistance, and it is what AC voltmeters and ammeters read and what "120 V" or "440 V" ratings mean. For a sine wave, RMS = 0.707 × peak, and conversely peak = 1.414 × RMS. The average value of one half-cycle is 0.637 × peak (the full-cycle average is zero). Instantaneous value is the amplitude at a specific instant. Phase describes the time relationship between two sine waves of the same frequency, measured in degrees of the 360° cycle. Waves that reach corresponding points together are in phase; otherwise one leads or lags the other…

NEETS Mod. 2 §4-1

NEETS Mod. 2 §4-1 — Reactance and impedance In AC circuits inductance and capacitance oppose current in a way that depends on frequency; this opposition is reactance, measured in ohms. Inductive reactance is XL = 2πfL — it increases with frequency and inductance, so an inductor passes low frequencies more easily than high. Capacitive reactance is XC = 1/(2πfC) — it decreases with frequency and capacitance, so a capacitor passes high frequencies more easily than low and blocks DC (infinite XC at zero frequency). Reactance and resistance combine into impedance (Z), the total opposition to AC, which cannot simply be added arithmetically because the reactive voltages are 90° out of phase with the resistive voltage. Instead they add vectorially: Z = √(R² + X²), where X is the net reactance (XL…

NEETS Mod. 2 §4-2

NEETS Mod. 2 §4-2 — Phase angle, power factor, and true vs apparent power The net reactance in an AC circuit forces the current out of phase with the voltage by a phase angle (θ). In an inductive circuit current lags voltage; in a capacitive circuit current leads. Only the in-phase (resistive) component of current does useful work, so AC power has three measures. Apparent power, the simple product of RMS volts and amps, is expressed in volt-amperes (VA or kVA) and sizes generators and cables. True (real) power, the power actually converted to work or heat, is in watts (or kW) and equals E × I × cos θ. Reactive power, expressed in VARs, is the power that oscillates into and out of the magnetic and electric fields doing no net work. Power factor is the ratio of true to apparent power, equal…

NEETS Mod. 3 §1-4

NEETS Mod. 3 §1-4 — Wattmeters, frequency meters, and instrument accuracy Power in an AC circuit is measured with a wattmeter, which uses two coils: a low-resistance current coil in series with the load and a high-resistance voltage (potential) coil across it. The instrument's deflection is proportional to the product of voltage, current, and the cosine of the phase angle, so it reads true power in watts directly, automatically accounting for power factor — something a simple volt-times-amp calculation cannot do. On large switchboards, current and potential transformers feed the wattmeter safely from high-current, high-voltage buses. Frequency is monitored with a frequency meter (vibrating-reed or pointer type) to keep generators at the correct 50/60 Hz, which is essential before parallel…