Comprehensive notes for Chapter 16 Alternating Current. Covers AC fundamentals, AC through Resistors, Capacitors, Inductors, Impedance, Resonance, Three Phase Supply, and EM Waves with Modulation.
Alternating Current (AC): The current which changes its magnitude continuously and direction periodically.
Instantaneous Value: Value at any time t. $$ V = V_o \sin \omega t $$
Peak Value ($$ V_o $$): The highest value reached in one cycle.
Peak-to-Peak Value: Sum of positive and negative peak values ($$ 2V_o $$).
Root Mean Square (RMS) Value: The effective value of DC that produces the same heating effect. $$ V_{rms} = \frac{V_o}{\sqrt{2}} = 0.707 V_o $$
Phase Lag/Lead: If voltage reaches maximum before current, voltage leads. If after, it lags.
In a pure resistive circuit, voltage and current are in phase.
$$ V = V_o \sin \omega t $$
$$ I = I_o \sin \omega t $$
Power: $$ P = V_{rms} I_{rms} $$
Current leads voltage by $$ \pi/2 $$ (90 degrees). capacitor blocks DC but allows AC.
Reactance ($$ X_C $$): Opposition offered by capacitor. $$ X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} $$
Power dissipated in pure capacitor is zero.
Voltage leads current by $$ \pi/2 $$ (90 degrees). Opposes change in current (Lenz's Law).
Reactance ($$ X_L $$): Opposition offered by inductor. $$ X_L = \omega L = 2\pi f L $$
Power dissipated in pure inductor is zero.
Combined effect of resistance and reactance in an AC circuit. Denoted by Z. Unit is Ohm.
$$ Z = \frac{V_{rms}}{I_{rms}} $$
RC Series Circuit: $$ Z = \sqrt{R^2 + X_C^2} $$
RL Series Circuit: $$ Z = \sqrt{R^2 + X_L^2} $$
Power is consumed only in resistance. No power loss in pure L or C over a cycle.
Power Factor: $$ P = V_{rms} I_{rms} \cos \theta $$
Here, $$ \cos \theta = \frac{R}{Z} $$ is the Power Factor.
Series Resonance (Acceptor): Current is maximum at $$ f_r $$. $$ Z = R $$ (minimum). $$ f_r = \frac{1}{2\pi \sqrt{LC}} $$
Parallel Resonance (Rejector): Current is minimum (Rejector) at $$ f_r $$. Impedance is maximum.
Uses three coils inclined at 120 degrees. Voltage across each phase is phase-shifted by 120 degrees.
Voltage: Line voltage $$ V_L = \sqrt{3} V_{phase} $$. Total load is distributed.
Changing electric flux creates magnetic field and vice versa. Propagate through space without medium.
Speed: $$ c = \frac{1}{\sqrt{\mu_o \epsilon_o}} = 3 \times 10^8 m/s $$
Spectrum: Radio, Micro, IR, Visible, UV, X-Rays, Gamma Rays.
Combining low frequency signal with high frequency carrier wave.
Amplitude Modulation (AM): Amplitude of carrier changes. (540 kHz - 1600 kHz).
Frequency Modulation (FM): Frequency of carrier changes. (88 MHz - 108 MHz). Better quality, less interference.