AC Waveforms and Power Factor Quiz

Waveforms:
- AC waveforms are typically sinusoidal, but can also be triangular or square.
- A sinusoidal waveform is defined by its amplitude (maximum value) and frequency (number of cycles per second).
Frequency:
- Measured in Hertz (Hz); 1 Hz = 1 cycle per second.
- Common AC frequency in households: 50 Hz or 60 Hz, depending on the country.
- Angular Frequency (ω): ω = 2πf, where f is the frequency in Hz.

Power Factor (PF):
- Ratio of real power (measured in watts) to apparent power (measured in volt-amperes).
- PF = cos(φ), where φ is the phase angle between voltage and current.
- PF values range from 0 to 1; a higher PF indicates efficient use of electricity.
Impedance (Z):
- Total opposition to AC current, comprising resistance (R) and reactance (X).
- Z is expressed as a complex number: Z = R + jX.
- Reactance can be inductive (XL = ωL) or capacitive (XC = 1/ωC).

Ohm's Law: V = IZ applies to AC circuits, where I is the current and Z is the impedance.
Kirchhoff's Laws:
- Voltage Law: The sum of voltages around a closed loop is zero.
- Current Law: The sum of currents entering a junction equals the sum of currents leaving.
Phasors:
- Represent AC voltages and currents as rotating vectors in a complex plane.
- Simplifies calculations by converting differential equations into algebraic equations.
Series and Parallel Circuits:
- In series: Total impedance Z = Z1 + Z2 + ... + Zn.
- In parallel: Total impedance 1/Z = 1/Z1 + 1/Z2 + ... + 1/Zn.

Function: Transfer electrical energy between circuits, converting voltages and currents.
Types:
- Step-up transformer: Increases voltage, decreases current.
- Step-down transformer: Decreases voltage, increases current.
Operation:
- Based on electromagnetic induction; primary coil generates a magnetic field that induces voltage in the secondary coil.
Efficiency:
- Typically high (95-99%); losses occur mainly due to resistance in the windings and core losses (hysteresis and eddy current losses).
Voltage Transformation Ratio:
- Vp/Vs = Np/Ns, where Vp and Vs are primary and secondary voltages, and Np and Ns are the number of turns in the primary and secondary coils, respectively.

AC waveforms can be sinusoidal, triangular, or square in shape.
Sinusoidal waveforms are characterized by amplitude (maximum value) and frequency (cycles per second).
Frequency is measured in Hertz (Hz); 1 Hz equals 1 cycle per second.
Household AC frequency typically ranges from 50 Hz to 60 Hz, varying by country.
Angular frequency (ω) is calculated using the formula ω = 2πf, where f represents frequency in Hz.

Power Factor (PF) is the ratio of real power (watts) to apparent power (volt-amperes).
PF is given by the formula PF = cos(φ), with φ being the phase angle between voltage and current.
PF values range between 0 (inefficient) and 1 (efficient); higher values signify better electrical efficiency.
Impedance (Z) represents total opposition to AC current, combining resistance (R) and reactance (X).
Z is expressed in complex form: Z = R + jX, where j is the imaginary unit.
Reactance has two forms: inductive (XL = ωL) and capacitive (XC = 1/ωC).

Ohm's Law for AC circuits is expressed as V = IZ, relating voltage (V), current (I), and impedance (Z).
Kirchhoff's Voltage Law asserts that the sum of all voltages in a closed loop equals zero.
Kirchhoff's Current Law states that the total current entering a junction equals the total current exiting.
Phasors are used to represent AC voltages and currents as rotating vectors in a complex plane, simplifying calculations.
In series circuits, total impedance is calculated as Z = Z1 + Z2 + ... + Zn.
In parallel circuits, total impedance is found using the formula 1/Z = 1/Z1 + 1/Z2 + ... + 1/Zn.

Transformers transfer electrical energy between circuits and modify voltages and currents.
Step-up transformers increase voltage and decrease current, while step-down transformers decrease voltage and increase current.
Transformers operate on the principle of electromagnetic induction; the primary coil generates a magnetic field that induces voltage in the secondary coil.
Typical transformer efficiency is high, ranging from 95% to 99%, with losses from winding resistance and core losses (hysteresis and eddy currents).
The voltage transformation ratio is expressed as Vp/Vs = Np/Ns, where Vp and Vs are the primary and secondary voltages, and Np and Ns are the respective number of turns in the coils.