AC Circuits

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Q1. In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and capacitance is 50μF, what is the total admittance? (2022)

Solution:

Total admittance Y = 1/R + j(ωC - 1/ωL). Calculate Y using given values.

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Q2. What is the power factor of a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

Solution:

Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.

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Q3. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50Ω, what is the current? (2021)

Solution:

Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.

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Q4. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)

Solution:

Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.

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Q5. What is the impedance of a circuit with a resistance of 4Ω and a reactance of 3Ω? (2020)

Solution:

Impedance Z = √(R² + X²) = √(4² + 3²) = √(16 + 9) = √25 = 5Ω.

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Q6. In a parallel RLC circuit, if the resistance is 10Ω, inductance is 0.2H, and capacitance is 50μF, what is the total current at resonance? (2022)

Solution:

At resonance, total current I = V/R. Calculate using V = 10V.

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Q7. In an RLC series circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)

Solution:

Using f = 1/(2π√(LC)), we find f = 1/(2π√(0.1 * 100e-6)) ≈ 159 Hz.

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Q8. What is the power consumed in an AC circuit with a voltage of 230V and a current of 5A with a power factor of 0.8? (2023)

Solution:

Power = V × I × Power Factor = 230V × 5A × 0.8 = 920W.

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Q9. What is the power factor of a circuit with a resistance of 6Ω and a reactance of 8Ω? (2022)

Solution:

Power factor = R/Z = R/√(R² + X²) = 6/√(6² + 8²) = 6/10 = 0.6.

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Q10. A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedance of the circuit? (2020)

Solution:

The impedance Z = √(R² + X²) = √(10² + 10²) = √200 = 14.14 Ω.