JEE Main - Reactance, impedance and LCR series resonance Online Test (MCQ Quiz)

1. What is the unit of reactance in the SI system?

A) Henry (H) B) Farad (F) C) Ohm (Ω) D) Siemens (S)

2. Which component in an AC circuit primarily causes inductive reactance?

A) Resistor B) Capacitor C) Inductor D) Diode

3. What is the formula for inductive reactance (XL)?

A) XL = 1 / (ωC) B) XL = R C) XL = ωL D) XL = Z

4. Which component in an AC circuit primarily causes capacitive reactance?

A) Resistor B) Capacitor C) Inductor D) Transformer

5. What is the formula for capacitive reactance (XC)?

A) XC = 1 / (ωC) B) XC = R C) XC = ωL D) XC = Z

6. In an AC circuit, what does 'ω' represent?

A) Angular frequency B) Frequency C) Wavelength D) Amplitude

7. What is impedance (Z) in an AC circuit?

A) The total opposition to current flow, including resistance and reactance B) Only the resistance of the circuit C) Only the reactance of the circuit D) The voltage across the circuit

8. How is impedance (Z) related to resistance (R), inductive reactance (XL), and capacitive reactance (XC) in a series LCR circuit?

A) Z = R + XL + XC B) Z = sqrt(R^2 + (XL - XC)^2) C) Z = R * XL * XC D) Z = R / (XL - XC)

9. At resonance in a series LCR circuit, what is the relationship between inductive reactance (XL) and capacitive reactance (XC)?

A) XL > XC B) XL < XC C) XL = XC D) XL = 0

10. What is the condition for resonance in a series LCR circuit in terms of angular frequency (ω)?

A) ω = 1 / sqrt(LC) B) ω = sqrt(LC) C) ω = LC D) ω = 1 / LC

11. At resonance, what is the value of the impedance (Z) in a series LCR circuit?

A) Z = infinity B) Z = 0 C) Z = R D) Z = XL

12. What is the significance of resonance in a series LCR circuit?

A) The current is minimum B) The impedance is maximum C) The current is maximum for a given voltage D) The circuit behaves purely inductively

13. The resonant frequency (f0) of a series LCR circuit is related to the resonant angular frequency (ω0) by:

A) f0 = ω0 / π B) f0 = 2π / ω0 C) f0 = ω0 / (2π) D) f0 = π / ω0

14. If the frequency of the AC source is increased above the resonant frequency in a series LCR circuit, the circuit behaves:

A) Capacitively B) Inductively C) Resistively D) Like a short circuit

15. If the frequency of the AC source is decreased below the resonant frequency in a series LCR circuit, the circuit behaves:

A) Capacitively B) Inductively C) Resistively D) Like an open circuit

16. What is the unit of inductance (L) in the SI system?

A) Ohm (Ω) B) Farad (F) C) Henry (H) D) Watt (W)

17. What is the unit of capacitance (C) in the SI system?

A) Henry (H) B) Ohm (Ω) C) Farad (F) D) Volt (V)

18. In a series LCR circuit, if R = 0, then at resonance, the impedance Z is:

A) R B) XL C) XC D) Zero

19. The quality factor (Q) of a series resonance circuit is defined as:

A) R / (ω0L) B) (ω0L) / R C) R / (ω0C) D) (ω0C) / R

20. A high Q-factor in a resonance circuit indicates:

A) A very broad resonance curve B) A sharp resonance curve with a narrow bandwidth C) Low selectivity D) High impedance at all frequencies

21. The bandwidth (Δω) of a series resonance circuit is given by:

A) ω0 / Q B) Q / ω0 C) R / L D) L / R

22. In a series LCR circuit, if the frequency of the source is doubled, how does the inductive reactance change?

A) It remains the same B) It is halved C) It is doubled D) It becomes zero

23. In a series LCR circuit, if the frequency of the source is doubled, how does the capacitive reactance change?

A) It remains the same B) It is halved C) It is doubled D) It becomes infinite

24. What is the phase difference between voltage across the inductor and current through it in an AC circuit?

A) Zero B) π/2 (90 degrees) leading C) π/2 (90 degrees) lagging D) π (180 degrees)

25. What is the phase difference between voltage across the capacitor and current through it in an AC circuit?

A) Zero B) π/2 (90 degrees) leading C) π/2 (90 degrees) lagging D) π (180 degrees)

26. In a series LCR circuit, the voltage across the resistor is in phase with:

A) The source voltage B) The current C) The voltage across the inductor D) The voltage across the capacitor

27. At resonance, the power factor of a series LCR circuit is:

A) 0 B) 1/√2 C) 1 D) Infinity

28. If L = 2 H, C = 8 μF, and R = 10 Ω, calculate the resonant angular frequency (ω0).

A) 250 rad/s B) 500 rad/s C) 1000 rad/s D) 2000 rad/s

29. For a given L and C, the resonant frequency is inversely proportional to:

A) sqrt(LC) B) 1/sqrt(LC) C) LC D) 1/LC

30. In a series LCR circuit, the impedance is minimum at resonance. This means the current will be:

A) Minimum B) Maximum C) Zero D) Variable

31. What is the unit of power factor?

A) Ohm B) Ampere C) Volt D) Dimensionless

32. The impedance of a circuit is given by Z = sqrt(R^2 + X^2), where X is the net reactance. What is X?

A) XL + XC B) XL - XC C) XC - XL D) R

33. If a capacitor is added in series to a resonant RLC circuit, what happens to the resonant frequency?

A) Increases B) Decreases C) Remains the same D) Becomes zero

34. If an inductor is added in series to a resonant RLC circuit, what happens to the resonant frequency?

A) Increases B) Decreases C) Remains the same D) Becomes infinite

35. What is the condition for resonance in terms of frequency (f)?

A) f = 1 / (2π * sqrt(LC)) B) f = 2π * sqrt(LC) C) f = sqrt(LC) / (2π) D) f = 1 / (2π * LC)

36. The impedance of a purely inductive circuit is called:

A) Resistance B) Capacitive reactance C) Inductive reactance D) Admittance

37. The impedance of a purely capacitive circuit is called:

A) Resistance B) Capacitive reactance C) Inductive reactance D) Conductance

38. In a series LCR circuit, resonance occurs when the phase angle between the applied voltage and the current is:

A) π/2 (90 degrees) B) π (180 degrees) C) 0 D) π/4 (45 degrees)

39. Which of the following is NOT a unit of impedance or reactance?

A) Ohm B) Volt/Ampere C) Henry/Farad D) Watt

40. If the frequency of the AC source is very low (approaching zero), a series LCR circuit behaves predominantly as:

A) Inductive B) Capacitive C) Resistive D) A short circuit

41. If the frequency of the AC source is very high (approaching infinity), a series LCR circuit behaves predominantly as:

A) Inductive B) Capacitive C) Resistive D) An open circuit

42. The quantity 1/(ωC) is known as:

A) Inductive reactance B) Resistance C) Capacitive reactance D) Impedance

43. The quantity ωL is known as:

A) Inductive reactance B) Capacitive reactance C) Resistance D) Impedance

44. In a series LCR circuit, the voltage across the inductor leads the current by:

A) 90 degrees B) 180 degrees C) 0 degrees D) 45 degrees

45. In a series LCR circuit, the voltage across the capacitor lags the current by:

A) 90 degrees B) 180 degrees C) 0 degrees D) 45 degrees

46. What is the resonant frequency of an LC circuit?

A) 1/(2πLC) B) sqrt(LC)/(2π) C) (2π)/sqrt(LC) D) sqrt(LC)

47. In a series LCR circuit at resonance, the current is determined by:

A) R only B) L only C) C only D) L, C, and R

48. If the resistance in a series LCR circuit is increased, the sharpness of the resonance curve:

A) Increases B) Decreases C) Remains unchanged D) Becomes zero

49. Which phenomenon is utilized in tuning a radio receiver?

A) Mutual induction B) Self-induction C) Electrical resonance D) Electromagnetic waves

50. The impedance of a series RLC circuit is Z = sqrt(R^2 + (ωL - 1/(ωC))^2). At resonance, the term (ωL - 1/(ωC)) becomes:

A) Maximum B) Minimum (Zero) C) Equal to R D) Equal to infinity

Reactance, impedance and LCR series resonance - Online Test

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