AC Steady-State Analysis: Phasors and Impedance Quiz Quiz

Explore key concepts in AC steady-state analysis with this quiz focusing on phasors, impedance, and the relationships within RLC circuits. Perfect for students and professionals aiming to reinforce understanding of phasor diagrams, impedance calculation, and the effects of frequency on circuit behavior.

1. Impedance Identification in Circuits

   In a series circuit with a 10-ohm resistor and a 20-ohm reactance inductor, what is the total impedance?

   1. 30 Ω
   2. 20 + j10 Ω
   3. 10 + j20 Ω
   4. 10 - j20 Ω

   Explanation: The impedance of a resistor is purely real, and the impedance of an inductor is purely imaginary (jωL). For a resistor and inductor in series, the total impedance is the sum: 10 Ω (real) plus j20 Ω (imaginary), which equals 10 + j20 Ω. '30 Ω' of option B ignores the imaginary component. '10 - j20 Ω' of option C would be correct for a capacitor, not an inductor. '20 + j10 Ω' of option D misplaces the real and imaginary parts.

2. Phasor Representation Understanding

   Which of the following best describes a phasor in AC circuit analysis?

   1. A fixed point on a real axis
   2. A mathematical constant for circuit calculations
   3. A rotating vector that represents sinusoidal voltage or current amplitude and phase
   4. A scalar quantity for DC voltage

   Explanation: A phasor is a rotating vector (complex number) that shows both the magnitude and phase of a sine wave, making AC analysis easier. Option B incorrectly refers to DC, which does not use phasors. Option C ignores the phase relationship critical in AC circuits. Option D, while containing mathematical terms, fails to specify the representation aspect of phasors.

3. Frequency Effect on Impedance

   If the frequency of the source in a series RL circuit is doubled, what happens to the overall impedance?

   1. It decreases
   2. It becomes zero
   3. It remains unchanged
   4. It increases

   Explanation: In a series RL circuit, the impedance increases with frequency because the inductive reactance (X_L = 2πfL) grows as frequency increases. If frequency doubles, the inductive reactance also doubles, resulting in greater total impedance. Option B is incorrect because impedance does not decrease with higher frequency in RL circuits. Option C is false as change in frequency affects inductive reactance. Option D, zero impedance, is only possible if both resistance and reactance are zero.

4. Voltage-Current Phase Relationship

   In a purely capacitive AC circuit, what is the phase difference between the voltage across the capacitor and the current through it?

   1. Current leads voltage by 90 degrees
   2. Voltage leads current by 90 degrees
   3. They are 180 degrees out of phase
   4. They are in phase

   Explanation: In a purely capacitive circuit, current leads voltage by 90 degrees. This happens because the changing voltage across a capacitor causes the current to flow ahead in phase. Option B is correct for inductors, not capacitors. Option C is incorrect because that applies to purely resistive circuits. Option D, 180 degrees, describes total opposition, which does not occur in ideal capacitive circuits.

5. Combining Impedances in Parallel

   How do you calculate the total impedance of two parallel branches, one with impedance Z1 and the other with impedance Z2, in an AC circuit?

   1. (Z1 + Z2) / (Z1 × Z2)
   2. Z1 × Z2
   3. (Z1 × Z2) / (Z1 + Z2)
   4. Z1 + Z2

   Explanation: The correct formula for the total impedance of two parallel impedances is (Z1 × Z2) / (Z1 + Z2). Option B is for series connection, not parallel. Option C incorrectly multiplies the impedances without considering the parallel nature. Option D inaccurately inverts the parallel impedance formula, which gives the wrong dimension.