Funda

Generation of Alternating Electromotive Force

Priority Definitions

  • Induced electromotive force (emf): Voltage created in a coil through changing magnetic flux according to Faraday's law.

  • Generated emf: Voltage generated by physical motion of the coil or magnet within a magnetic field.

  • Frequency (f): The number of cycles per second, measured in Hertz (Hz) with 1 Hz = 1 cycle per second.

  • Period (T): The time required for one complete cycle of an alternating current.

  • Wavelength (λ): The distance travelled by a wave in one cycle, calculated as λ = v/f.

Formulas

  1. Induced emf: [ e = N \left( \frac{d\phi}{dt} \right) \times 10^{-8} \text{ volts} ]

    • N: number of turns in the coil

    • dϕ/dt: rate at which flux changes through the coil in maxwells

  2. Generated emf:[ e = B(l)(v) \times 10^{-8} \text{ volts} ]

    • B: flux density (lines per square inch)

    • l: length of the wire (inches)

    • v: velocity of the wire (inches per second)

AC Generator Structure

  • Two-pole single AC generator illustrated with a coil moving through the magnetic field created by poles N and S.

  • Clockwise rotation:

    • One side of the coil moves downward, cutting maximum flux under N.

    • Opposite side moves upward, cutting maximum flux under S.

  • After 90° rotation: No flux cut, hence no voltage.

  • As rotation continues, the other side of the coil will begin to cut the maximum flux under the opposite pole.

Key Points During Coil Rotation

  • Voltage changes with each instant.

  • Electrical polarity alternates (+ and -) depending on the position under N and S poles.

Example Calculation of Average Induced Voltage

  • Given a coil of 300 turns with flux changing from 250,000 to 20,000 maxwells in 0.15 seconds:

Sine Wave Voltage Generation

  • Voltage in a generator is alternating where:

    • Magnitude varies from instant to instant as flux values change.

    • Direction changes due to coil side positions under north and south poles.

  • Maximum voltage and diminishing voltage illustrated in sine wave forms.

General induced voltage formula:

[ V = Em \sin( \theta ) ]

Frequency and Time Relationship

  • Frequency (f) = number of cycles per second; unit: Hertz (Hz)

  • 1 Hz = 1 cycle per second.

  • Period (T) = time required for one cycle; f = 1/T.

  • Example: 60 revolutions in 1 second = 60 Hz.

Period calculation given frequency.

Frequency, Time, and Wavelength Relationships

  • Wavelength (λ) is the distance travelled by a wave in one cycle: [ \lambda = \frac{v}{f} \text{ (where } v = \text{ wave velocity, } f = \text{ frequency)} ]

  • Radio waves travel at the speed of light; sound waves velocity is lower.

AC Generator Basics

  • An alternator is described as an AC generator with cycles of voltage variations for each rotation.

  • Relationship between revolutions per second and frequency: [ f = \left( \frac{P}{2} \right) \times \text{ (revolutions per second)} ]

  • Electrical degrees representation for cycles (360° = one cycle).

Angular Velocity and Sinusoidal Functions

  • Voltage in a resistor, inductor, and capacitor behaves based on sinusoidal functions.

  • Current is dependent upon the emf and time, with the wave functions represented using sine and cosine functions.

Circuit Types in AC

  • Basic types of circuits: R (Resistor), L (Inductor), C (Capacitor).

  • Behavior in AC circuits:

    • Pure resistor: conducts as in DC circuits; current and voltage phase are equivalent.

    • Pure inductor: current lags voltage by 90°.

    • Pure capacitor: current leads voltage by 90°.

Example Problems and Calculations

  • Various scenarios discussing the relationships between voltage, current, and their phase differences in different circuits (R-L, R-C, R-L-C circuits) are provided with indications of how to calculate current, maximum power, voltage qualities, etc.

  • Complex circuit interactions are summarized, along with example problems for further practice.