🎢Principles of Physics II Unit 8 – AC Circuits & Electromagnetic Waves

Key Concepts and Definitions

• Alternating current (AC) involves the flow of electric charge that periodically reverses direction
• AC voltage source generates an oscillating voltage that varies sinusoidally with time
• Frequency (f) measures the number of cycles per second and is expressed in hertz (Hz)
• Period (T) represents the time required for one complete cycle and is the reciprocal of frequency ($T = 1/f$)
• Peak voltage ($V_p$) and peak current ($I_p$) define the maximum values in the AC waveform
  • RMS (root mean square) values, $V_{rms}$ and $I_{rms}$, are used for equivalent DC values ($V_{rms} = V_p/\sqrt{2}$, $I_{rms} = I_p/\sqrt{2}$)
• Phasors are complex numbers that represent the amplitude and phase of sinusoidal quantities
• Impedance (Z) is the AC equivalent of resistance, expressing the opposition to current flow in an AC circuit

AC Circuit Fundamentals

• AC circuits consist of resistors, capacitors, and inductors connected to an AC voltage source
• Resistors oppose current flow and cause voltage drops in phase with the current
• Capacitors store energy in an electric field and cause the current to lead the voltage by 90°
  • Capacitive reactance ($X_C$) decreases with increasing frequency ($X_C = 1/(2\pi fC)$)
• Inductors store energy in a magnetic field and cause the current to lag the voltage by 90°
  • Inductive reactance ($X_L$) increases with increasing frequency ($X_L = 2\pi fL$)
• Kirchhoff's voltage law (KVL) and current law (KCL) apply to AC circuits
• Ohm's law for AC circuits relates voltage, current, and impedance ($V = IZ$)

Components in AC Circuits

• Resistors have a constant impedance equal to their resistance ($Z_R = R$)
• Capacitors have an impedance that depends on frequency and capacitance ($Z_C = -j/(2\pi fC)$)
  • Capacitive reactance ($X_C$) represents the imaginary part of the capacitor's impedance
• Inductors have an impedance that depends on frequency and inductance ($Z_L = j2\pi fL$)
  • Inductive reactance ($X_L$) represents the imaginary part of the inductor's impedance
• Transformers consist of two coupled coils and are used to step up or step down AC voltages
  • Turns ratio ($N_p/N_s$) determines the voltage and current transformation
• Ideal transformers have no losses and maintain the same power on both sides

AC Circuit Analysis Techniques

• Phasor diagrams visually represent the relationships between voltage and current phasors
• Series AC circuits have the same current through all components, with voltages adding vectorially
  • Impedances in series add directly ($Z_{total} = Z_1 + Z_2 + ...$)
• Parallel AC circuits have the same voltage across all components, with currents adding vectorially
  • Admittances (Y) in parallel add directly ($Y_{total} = Y_1 + Y_2 + ...$), where $Y = 1/Z$
• Complex power (S) is the product of voltage and current phasors ($S = VI^*$)
  • Real power (P) is the real part of complex power and represents the average power dissipated
  • Reactive power (Q) is the imaginary part of complex power and represents the power exchanged between components

Power in AC Circuits

• Instantaneous power is the product of instantaneous voltage and current
• Average power is the mean value of instantaneous power over one cycle
  • For resistive loads, $P_{avg} = V_{rms}I_{rms}$
  • For reactive loads, $P_{avg} = V_{rms}I_{rms}\cos\theta$, where $\theta$ is the phase angle between voltage and current
• Power factor (PF) is the ratio of real power to apparent power ($PF = P/|S|$)
  • PF ranges from 0 (purely reactive) to 1 (purely resistive)
• Reactive power compensation techniques (capacitor banks) improve power factor and reduce losses

Resonance and Filters

• Resonance occurs when the inductive and capacitive reactances are equal in magnitude ($X_L = X_C$)
  • Series resonance results in minimum impedance and maximum current
  • Parallel resonance results in maximum impedance and minimum current
• Resonant frequency ($f_0$) depends on the circuit's inductance and capacitance ($f_0 = 1/(2\pi\sqrt{LC})$)
• Quality factor (Q) measures the sharpness of the resonance peak and the circuit's selectivity
• Filters are circuits designed to pass or block specific frequency ranges
  • Low-pass filters allow low frequencies to pass while attenuating high frequencies
  • High-pass filters allow high frequencies to pass while attenuating low frequencies
  • Band-pass filters allow a specific range of frequencies to pass while attenuating others
  • Band-stop (notch) filters attenuate a specific range of frequencies while allowing others to pass

Electromagnetic Waves: Basics

• Electromagnetic (EM) waves are oscillating electric and magnetic fields that propagate through space
• EM waves are generated by accelerating electric charges and changing currents
• Electric and magnetic fields in an EM wave are perpendicular to each other and the direction of propagation
• EM waves travel at the speed of light (c) in vacuum ($c \approx 3 \times 10^8$ m/s)
• Wavelength ($\lambda$) is the distance between two consecutive crests or troughs of the wave
• Frequency (f) and wavelength ($\lambda$) are related by the speed of light ($c = f\lambda$)
• EM spectrum categorizes EM waves based on their frequency and wavelength (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays)

EM Wave Properties and Behavior

• EM waves exhibit properties such as reflection, refraction, diffraction, and interference
• Reflection occurs when EM waves bounce off a surface, with the angle of incidence equal to the angle of reflection
• Refraction occurs when EM waves bend as they pass through a medium with a different refractive index
  • Snell's law relates the angles of incidence and refraction to the refractive indices of the media
• Diffraction is the bending of EM waves around obstacles or through openings
  • The amount of diffraction depends on the wavelength and the size of the obstacle or opening
• Interference is the superposition of two or more EM waves, resulting in constructive (amplitude addition) or destructive (amplitude subtraction) interference
• Polarization describes the orientation of the electric field in an EM wave
  • Linear polarization: electric field oscillates in a single plane
  • Circular and elliptical polarization: electric field rotates as the wave propagates

Applications and Real-World Examples

• Radio and television broadcasting use EM waves in the radio and microwave frequencies to transmit signals
• Wireless communication devices (cell phones, Wi-Fi routers) rely on EM waves to send and receive data
• Microwave ovens use EM waves to heat food by exciting water molecules
• Radar systems emit EM waves and analyze the reflected waves to determine the position and velocity of objects
• Medical imaging techniques (X-rays, MRI) utilize EM waves to create images of the body's internal structures
• Fiber optic communication uses light (EM waves) to transmit data through thin glass or plastic fibers
• Solar cells convert the energy of EM waves (sunlight) into electrical energy
• Remote sensing satellites use EM waves to gather data about the Earth's surface, atmosphere, and oceans