AC Circuits
Q. A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance? (2020)
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A.
5Ω
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B.
10Ω
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C.
√125Ω
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D.
√(10² + 5²)Ω
Solution
The impedance Z = √(R² + X²) = √(10² + 5²) = √125Ω.
Correct Answer: D — √(10² + 5²)Ω
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Q. A coil has an inductance of 0.5 H and is connected to a 50 Hz AC supply. What is the inductive reactance? (2020)
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A.
25.13 Ω
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B.
31.42 Ω
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C.
50 Ω
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D.
100 Ω
Solution
Inductive reactance Xl = 2πfL = 2π(50)(0.5) = 31.42 Ω.
Correct Answer: B — 31.42 Ω
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Q. If a capacitor is charged to 12V and has a capacitance of 6μF, what is the stored energy? (2022)
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A.
0.432 mJ
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B.
0.072 mJ
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C.
0.864 mJ
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D.
0.216 mJ
Solution
Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.
Correct Answer: A — 0.432 mJ
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Q. If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)
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A.
5 A
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B.
2.5 A
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C.
7.07 A
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D.
3.54 A
Solution
The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.
Correct Answer: B — 2.5 A
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Q. If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)
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A.
Doubles
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B.
Halves
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C.
Remains the same
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D.
Quadruples
Solution
Xl = 2πfL; if f is doubled, Xl also doubles.
Correct Answer: B — Halves
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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)
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A.
It doubles
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B.
It halves
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C.
It remains the same
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D.
It quadruples
Solution
Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.
Correct Answer: B — It halves
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Q. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)
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A.
It doubles
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B.
It halves
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C.
It remains the same
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D.
It quadruples
Solution
The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.
Correct Answer: B — It halves
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Q. If the inductance of a coil is 0.5H and the frequency is 60Hz, what is the inductive reactance? (2023)
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A.
31.42 ohms
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B.
18.85 ohms
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C.
37.70 ohms
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D.
25.13 ohms
Solution
Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.
Correct Answer: A — 31.42 ohms
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Q. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
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A.
10Ω
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B.
30Ω
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C.
33.33Ω
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D.
40Ω
Solution
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Correct Answer: C — 33.33Ω
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Q. If the total current in an AC circuit is 5A and the voltage is 120V, what is the impedance? (2023)
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A.
24Ω
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B.
20Ω
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C.
30Ω
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D.
15Ω
Solution
Impedance (Z) = Voltage (V) / Current (I) = 120V / 5A = 24Ω.
Correct Answer: B — 20Ω
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Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50Ω, what is the current through the capacitor? (2023)
Solution
Current (I) = Voltage (V) / Capacitive Reactance (XC) = 100V / 50Ω = 2A.
Correct Answer: B — 2A
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Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50Ω, what is the current? (2021)
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A.
2A
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B.
0.5A
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C.
5A
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D.
100A
Solution
Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.
Correct Answer: B — 0.5A
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Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50 ohms, what is the current? (2023)
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A.
2A
-
B.
0.5A
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C.
5A
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D.
10A
Solution
Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.
Correct Answer: A — 2A
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Q. If the voltage across a capacitor is 100V and the capacitive reactance is 50 ohms, what is the current through the capacitor? (2022)
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A.
2 A
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B.
1 A
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C.
0.5 A
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D.
0.25 A
Solution
I = V/Xc = 100/50 = 2 A.
Correct Answer: B — 1 A
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Q. If the voltage across a resistor is 240V and the resistance is 60 ohms, what is the current flowing through it? (2020)
Solution
I = V / R = 240V / 60Ω = 4A.
Correct Answer: C — 6A
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Q. In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the total admittance? (2023)
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A.
0.02 S
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B.
0.04 S
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C.
0.06 S
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D.
0.08 S
Solution
Y = 1/R + j(ωC - 1/ωL); calculate Y for given values.
Correct Answer: C — 0.06 S
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Q. In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the quality factor Q? (2015)
Solution
Quality factor Q = (1/R) * √(L/C) = (1/50) * √(0.2/50e-6) = 2.
Correct Answer: B — 2
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Q. In a purely capacitive AC circuit, the current leads the voltage by how many degrees? (2022)
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A.
0°
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B.
90°
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C.
180°
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D.
270°
Solution
In a purely capacitive circuit, the current leads the voltage by 90°.
Correct Answer: B — 90°
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Q. In a purely capacitive AC circuit, the current leads the voltage by how much phase angle? (2023)
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A.
0 degrees
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B.
90 degrees
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C.
180 degrees
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D.
270 degrees
Solution
In a purely capacitive circuit, the current leads the voltage by 90 degrees.
Correct Answer: B — 90 degrees
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Q. In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the resonant frequency? (2021)
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A.
159.15 Hz
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B.
100 Hz
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C.
50 Hz
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D.
200 Hz
Solution
f0 = 1 / (2π√(LC)) = 1 / (2π√(0.1 × 100 × 10^-6)) = 159.15 Hz.
Correct Answer: A — 159.15 Hz
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Q. In a series RLC circuit, if R = 20Ω, L = 0.1 H, and C = 100μF, what is the resonant frequency? (2020)
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A.
50 Hz
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B.
100 Hz
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C.
159.15 Hz
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D.
200 Hz
Solution
Resonant frequency f₀ = 1 / (2π√(LC)) = 1 / (2π√(0.1 * 100e-6)) = 159.15 Hz.
Correct Answer: C — 159.15 Hz
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Q. In a series RLC circuit, if the inductive reactance is greater than the capacitive reactance, the circuit is said to be: (2019)
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A.
Resonant
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B.
Capacitive
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C.
Inductive
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D.
Purely resistive
Solution
If inductive reactance (XL) is greater than capacitive reactance (XC), the circuit is inductive.
Correct Answer: C — Inductive
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Q. In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2021)
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A.
50 Hz
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B.
100 Hz
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C.
159 Hz
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D.
200 Hz
Solution
Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.
Correct Answer: C — 159 Hz
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Q. In a series RLC circuit, if the resistance is 10Ω, inductance is 0.1H, and capacitance is 100μF, what is the resonant frequency? (2021)
-
A.
50Hz
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B.
100Hz
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C.
159Hz
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D.
200Hz
Solution
Resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1*100e-6)) ≈ 159Hz.
Correct Answer: C — 159Hz
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Q. In an AC circuit, if the frequency is 60Hz and the inductance is 0.2H, what is the inductive reactance? (2021)
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A.
12.56Ω
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B.
37.68Ω
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C.
75.36Ω
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D.
100Ω
Solution
Inductive reactance (XL) = 2πfL = 2π(60)(0.2) ≈ 75.36Ω.
Correct Answer: B — 37.68Ω
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Q. In an AC circuit, if the power factor is 0.8, what is the angle between the voltage and current? (2020)
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A.
36.87°
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B.
53.13°
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C.
60°
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D.
45°
Solution
The angle θ can be found using cos(θ) = power factor. Therefore, θ = cos⁻¹(0.8) ≈ 36.87°.
Correct Answer: B — 53.13°
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Q. In an AC circuit, if the resistance is 10 ohms and the inductive reactance is 20 ohms, what is the impedance? (2020)
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A.
10 ohms
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B.
20 ohms
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C.
√(10² + 20²)
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D.
30 ohms
Solution
The impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36 ohms.
Correct Answer: C — √(10² + 20²)
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Q. In an AC circuit, if the voltage is 120 V and the current is 10 A with a power factor of 0.8, what is the real power consumed? (2021)
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A.
960 W
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B.
1200 W
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C.
800 W
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D.
1000 W
Solution
Real power P = V * I * power factor = 120 * 10 * 0.8 = 960 W.
Correct Answer: A — 960 W
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Q. In an AC circuit, if the voltage is 120V and the current is 10A, what is the power factor if the real power is 600W? (2022)
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A.
0.5
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B.
0.6
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C.
0.8
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D.
1.0
Solution
Power factor = Real Power / (Voltage x Current) = 600 / (120 x 10) = 600 / 1200 = 0.5.
Correct Answer: B — 0.6
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Q. In an AC circuit, if the voltage is given by V(t) = 100 sin(100t), what is the RMS voltage? (2023)
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A.
100 V
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B.
70.7 V
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C.
50 V
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D.
141.4 V
Solution
The RMS voltage is V_rms = V0/√2 = 100/√2 = 70.7 V.
Correct Answer: B — 70.7 V
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