AC Circuits

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Q1. What is the phase difference between the voltage and current in a series RLC circuit at resonance? (2023)

Solution:

At resonance in a series RLC circuit, the phase difference between voltage and current is 0°.

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Q2. In an RLC circuit, if the inductive reactance is 10Ω and capacitive reactance is 5Ω, what is the net reactance? (2020)

Solution:

Net reactance = XL - XC = 10Ω - 5Ω = 5Ω.

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Q3. In an AC circuit, if the frequency is increased, what happens to the inductive reactance? (2020)

Solution:

Inductive reactance (XL = 2πfL) increases with an increase in frequency.

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Q4. What is the impedance of a circuit with a resistance of 4 ohms and a reactance of 3 ohms? (2021)

Solution:

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

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Q5. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)

Solution:

Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.

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Q6. What is the formula for the total impedance in a series RLC circuit? (2023)

Solution:

The total impedance in a series RLC circuit is given by Z = R + j(XL - XC).

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Q7. If the voltage across a capacitor is 100V and the capacitive reactance is 50 ohms, what is the current through the capacitor? (2022)

Solution:

I = V/Xc = 100/50 = 2 A.

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Q8. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)

Solution:

The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.

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Q9. In an AC circuit, if the voltage is V(t) = 120 sin(ωt), what is the RMS voltage? (2017)

Solution:

RMS voltage V_rms = V_peak / √2 = 120 / √2 = 84.85 V.

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Q10. If the total impedance in an AC circuit is 20Ω and the current is 2A, what is the voltage across the circuit? (2023)

Solution:

Using Ohm's law, V = IZ = 2A * 20Ω = 40V.