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Chapter 7: Alternating Current - Foundation Drill (Level 0)
Topic 7.1: Average and RMS Values
1.
The average value of alternating current over one complete cycle is exactly ____________.
2.
The RMS (Root Mean Square) value of alternating current is also known as the ____________ value.
3.
Which of the following relations between RMS current ($I_{rms}$) and peak current ($I_0$) is correct?
(A) $I_{rms} = \sqrt{2} I_0$ (B) $I_{rms} = I_0 / \sqrt{2}$ (C) $I_{rms} = I_0 / 2$ (D) $I_{rms} = 2 I_0$
(A) $I_{rms} = \sqrt{2} I_0$ (B) $I_{rms} = I_0 / \sqrt{2}$ (C) $I_{rms} = I_0 / 2$ (D) $I_{rms} = 2 I_0$
4.
When we say our domestic AC power supply is "$220\text{ V}$", this value specifically represents the:
(A) Peak voltage (B) Mean voltage (C) RMS voltage (D) Instantaneous voltage
(A) Peak voltage (B) Mean voltage (C) RMS voltage (D) Instantaneous voltage
5.
Define the Root Mean Square (RMS) value of alternating current in terms of heating effect.
6.
If the peak value of an alternating current is $14.14\text{ A}$, calculate its RMS value. (Take $\sqrt{2} \approx 1.414$).
7.
Calculate the peak voltage of a $220\text{ V}$ RMS domestic AC supply.
8.
Match the AC terms to their correct mathematical formulas:
| (a) $I_{avg}$ (Over half cycle) | (i) Zero |
| (b) $I_{avg}$ (Over full cycle) | (ii) $I_0 / \sqrt{2}$ |
| (c) $I_{rms}$ | (iii) $2 I_0 / \pi$ |
Topic 7.2: AC applied to Pure R, L, and C
9.
In a purely resistive AC circuit, the alternating voltage and alternating current are entirely in ____________ with each other.
10.
In a purely inductive AC circuit, the voltage ____________ the current by a phase angle of $\pi/2$ radians ($90^\circ$).
11.
In a purely capacitive AC circuit, the current ____________ the voltage by a phase angle of $\pi/2$ radians ($90^\circ$).
12.
What is the phase difference between voltage and current in a purely inductive circuit?
(A) $0$ (B) $\pi/4$ (C) $\pi/2$ (D) $\pi$
(A) $0$ (B) $\pi/4$ (C) $\pi/2$ (D) $\pi$
13.
What is a phasor in the context of Alternating Current?
14.
If the applied voltage to a pure capacitor is $V = V_0 \sin(\omega t)$, write the standard equation for the instantaneous alternating current $I$.
15.
Based on the phasor diagram concept described above, which phasor (Voltage or Current) rotates ahead in a pure inductor?
AI Image Prompt:
A clear phasor diagram for a purely inductive AC circuit. Draw a 2D Cartesian coordinate system. A phasor vector labeled 'I_0' (current) is drawn in the first quadrant at an angle omega*t from the X-axis. A second phasor vector labeled 'V_0' (voltage) is drawn leading the 'I_0' vector by exactly 90 degrees (pi/2) counter-clockwise. Standard physics notation. The background of the whole image should be fully white, in landscape mode, mathematically correct, and high quality.
Filename: Level0_Q15_PhasorInductor.jpg
16.
An alternating voltage is given by $V = 100 \sin(314 t)$. Calculate the frequency of the AC supply. (Take $\pi \approx 3.14$).
17.
Match the circuit elements to their voltage-current phase relationships:
| (a) Pure Resistor | (i) Current leads Voltage by $90^\circ$ |
| (b) Pure Inductor | (ii) Voltage leads Current by $90^\circ$ |
| (c) Pure Capacitor | (iii) Voltage and Current are in phase |
Topic 7.3: Reactance and Impedance
18.
The SI unit of both Inductive Reactance ($X_L$) and Capacitive Reactance ($X_C$) is the ____________.
19.
Inductive reactance ($X_L$) is directly proportional to the AC frequency, whereas capacitive reactance ($X_C$) is ____________ proportional to the AC frequency.
20.
What is the formula for the impedance ($Z$) of a series LCR circuit?
(A) $Z = R + X_L + X_C$ (B) $Z = \sqrt{R^2 + (X_L + X_C)^2}$ (C) $Z = \sqrt{R^2 + (X_L - X_C)^2}$ (D) $Z = R^2 + X_L^2 - X_C^2$
(A) $Z = R + X_L + X_C$ (B) $Z = \sqrt{R^2 + (X_L + X_C)^2}$ (C) $Z = \sqrt{R^2 + (X_L - X_C)^2}$ (D) $Z = R^2 + X_L^2 - X_C^2$
21.
Define Impedance ($Z$) in an AC circuit.
22.
Calculate the inductive reactance ($X_L$) of a $0.1\text{ H}$ inductor connected to a $50\text{ Hz}$ AC source. (Take $\pi \approx 3.14$).
23.
Calculate the capacitive reactance ($X_C$) of a $10\text{ }\mu\text{F}$ capacitor at an angular frequency $\omega = 100\text{ rad/s}$.
24.
Find the total impedance ($Z$) of a series LCR circuit if Resistance $R = 3\text{ }\Omega$, Inductive reactance $X_L = 8\text{ }\Omega$, and Capacitive reactance $X_C = 4\text{ }\Omega$.
25.
In the series LCR circuit shown above, which physical quantity remains exactly the same for all three components (L, C, and R) at any instant?
AI Image Prompt:
A clear schematic diagram of a standard Series LCR AC circuit. An AC voltage source symbol (a circle with a sine wave inside) is connected in series with an Inductor (L, coiled wire), a Capacitor (C, two parallel lines), and a Resistor (R, zigzag line). The components are labeled L, C, and R. The background of the whole image should be fully white, in landscape mode, mathematically correct, and high quality.
Filename: Level0_Q25_SeriesLCR.jpg
26.
Match the physical quantities to their correct formulas:
| (a) Inductive Reactance ($X_L$) | (i) $1 / (\omega C)$ |
| (b) Capacitive Reactance ($X_C$) | (ii) $\omega L$ |
| (c) Angular Frequency ($\omega$) | (iii) $2\pi f$ |
Topic 7.4: Resonance
27.
Electrical resonance occurs in a series LCR circuit when the inductive reactance ($X_L$) becomes exactly ____________ to the capacitive reactance ($X_C$).
28.
At resonance, the total impedance ($Z$) of a series LCR circuit is completely resistive and is at its ____________ (minimum/maximum) value.
29.
The formula for the resonant frequency ($f_r$) of a series LCR circuit is:
(A) $1 / \sqrt{LC}$ (B) $1 / (2\pi\sqrt{LC})$ (C) $2\pi / \sqrt{LC}$ (D) $\sqrt{LC} / 2\pi$
(A) $1 / \sqrt{LC}$ (B) $1 / (2\pi\sqrt{LC})$ (C) $2\pi / \sqrt{LC}$ (D) $\sqrt{LC} / 2\pi$
30.
At the condition of resonance in a series LCR circuit, the current flowing through the circuit is:
(A) Minimum (B) Maximum (C) Zero (D) Infinite
(A) Minimum (B) Maximum (C) Zero (D) Infinite
31.
Define the Quality Factor (Q-factor) of a resonant LCR circuit in simple terms.
32.
What is meant by the "sharpness of resonance"?
33.
Calculate the resonant angular frequency ($\omega_r$) if $L = 1\text{ H}$ and $C = 1\text{ }\mu\text{F}$ in a series circuit.
34.
Find the Q-factor of a series LCR circuit if the inductive reactance at resonance is $1000\text{ }\Omega$ and the circuit resistance is $10\text{ }\Omega$.
35.
Match the resonance conditions correctly:
| (a) Impedance at resonance | (i) $0^\circ$ (Voltage and Current in phase) |
| (b) Voltages $V_L$ and $V_C$ | (ii) $Z = R$ |
| (c) Phase difference ($\phi$) | (iii) Equal in magnitude, opposite in phase |
Topic 7.5: Power in AC Circuit
36.
The Power Factor of an AC circuit is defined as the ____________ of the phase angle ($\phi$) between voltage and current.
37.
A current is called "wattless current" when the average power dissipated in the circuit is strictly ____________.
38.
The power factor of a purely resistive circuit is:
(A) Zero (B) $0.5$ (C) $1$ (Unity) (D) Infinity
(A) Zero (B) $0.5$ (C) $1$ (Unity) (D) Infinity
39.
The power factor of a purely inductive or purely capacitive circuit is:
(A) Zero (B) $0.5$ (C) $1$ (Unity) (D) Infinity
(A) Zero (B) $0.5$ (C) $1$ (Unity) (D) Infinity
40.
Write the formula for the average power ($P_{avg}$) dissipated in a general series LCR circuit over a complete cycle.
41.
Write the formula for Power Factor ($\cos\phi$) in terms of Resistance ($R$) and Impedance ($Z$).
42.
Calculate the power factor of a series AC circuit if its resistance is $4\text{ }\Omega$ and total impedance is $5\text{ }\Omega$.
43.
Based on the Power Triangle above, the ratio of True Power to Apparent Power gives which important circuit parameter?
AI Image Prompt:
A right-angled Power Triangle diagram. The horizontal base is labeled 'True Power (P)'. The vertical perpendicular side is labeled 'Reactive Power (Q)'. The hypotenuse is labeled 'Apparent Power (S)'. The angle between the base and the hypotenuse is labeled with the Greek letter phi (φ). The background of the whole image should be fully white, in landscape mode, mathematically correct, and high quality.
Filename: Level0_Q43_PowerTriangle.jpg
44.
Match the circuit types to their respective power factors:
| (a) Purely Resistive Circuit | (i) $\cos\phi = R / Z$ |
| (b) Purely Inductive Circuit | (ii) $\cos\phi = 1$ |
| (c) Series LCR Circuit | (iii) $\cos\phi = 0$ |
Topic 7.6: LC Oscillations
45.
In LC oscillations, energy oscillates continuously between the electric field of the capacitor and the ____________ field of the inductor.
46.
Assuming zero resistance, the total energy in an ideal LC oscillating circuit remains completely ____________.
47.
The natural angular frequency ($\omega$) of an ideal LC oscillating circuit is:
(A) $\sqrt{LC}$ (B) $1 / \sqrt{LC}$ (C) $L/C$ (D) $C/L$
(A) $\sqrt{LC}$ (B) $1 / \sqrt{LC}$ (C) $L/C$ (D) $C/L$
48.
Write the standard formula for the electrostatic energy stored in a fully charged capacitor $C$ having a maximum charge $Q_0$.
49.
Write the standard formula for the magnetic energy stored in an inductor $L$ carrying a maximum current $I_0$.
50.
If the maximum charge on the capacitor in an LC circuit is $Q_0 = 4\text{ mC}$ and capacitance is $C = 2\text{ mF}$, calculate the total energy of the oscillating system.
51.
Match the electrical parameters of LC oscillations to their Mechanical spring-mass analogies:
| (a) Inductance ($L$) | (i) Displacement ($x$) |
| (b) Inverse of Capacitance ($1/C$) | (ii) Mass ($m$ / Inertia) |
| (c) Charge ($q$) | (iii) Spring constant ($k$) |
Topic 7.7: Transformers
52.
A transformer works purely on the principle of ____________ induction.
53.
A step-up transformer increases the AC voltage but simultaneously decreases the AC ____________.
54.
The iron core of a transformer is laminated heavily to minimize energy losses due to:
(A) Flux leakage (B) Eddy currents (C) Hysteresis (D) Copper loss
(A) Flux leakage (B) Eddy currents (C) Hysteresis (D) Copper loss
55.
For a step-down transformer, the turns ratio ($N_s / N_p$) is:
(A) Greater than 1 (B) Less than 1 (C) Equal to 1 (D) Infinite
(A) Greater than 1 (B) Less than 1 (C) Equal to 1 (D) Infinite
56.
Can a transformer be used to step up a steady DC voltage? Give a simple one-line reason.
57.
Write the primary transformer equation relating primary/secondary voltages ($V_p, V_s$) to primary/secondary turns ($N_p, N_s$).
58.
A transformer has $100$ turns in the primary coil and $500$ turns in the secondary coil. If the primary voltage is $220\text{ V}$, calculate the secondary voltage.
59.
For an ideal $100\%$ efficient transformer, Power Input = Power Output ($V_p I_p = V_s I_s$). If $V_p = 100\text{ V}$, $I_p = 2\text{ A}$, and $V_s = 200\text{ V}$, calculate the secondary current $I_s$.
60.
Match the transformer energy losses to their standard remedies:
| (a) Eddy Current Loss | (i) Using thick copper wires |
| (b) Hysteresis Loss | (ii) Laminated iron core |
| (c) Copper Loss ($I^2R$) | (iii) Using soft iron core |