JEE Main - Reactance, impedance and LCR series resonance Question Bank with Options

1. 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

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

A) Mutual induction

B) Self-induction

C) Electrical resonance

D) Electromagnetic waves

3. 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

4. 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

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

A) 1/(2πLC)

B) sqrt(LC)/(2π)

C) (2π)/sqrt(LC)

D) sqrt(LC)

6. 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

7. 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

8. The quantity ωL is known as:

A) Inductive reactance

B) Capacitive reactance

C) Resistance

D) Impedance

9. The quantity 1/(ωC) is known as:

A) Inductive reactance

B) Resistance

C) Capacitive reactance

D) Impedance

10. 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

11. 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

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

A) Ohm

B) Volt/Ampere

C) Henry/Farad

D) Watt

13. 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)

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

A) Resistance

B) Capacitive reactance

C) Inductive reactance

D) Conductance

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

A) Resistance

B) Capacitive reactance

C) Inductive reactance

D) Admittance

16. 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)

17. 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

18. 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

19. 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

20. What is the unit of power factor?

A) Ohm

B) Ampere

C) Volt

D) Dimensionless

21. 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

22. 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

23. 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

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

A) 0

B) 1/√2

C) 1

D) Infinity

25. 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

26. 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)

27. 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)

28. 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

29. 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

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

A) ω0 / Q

B) Q / ω0

C) R / L

D) L / R

31. 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

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

A) R / (ω0L)

B) (ω0L) / R

C) R / (ω0C)

D) (ω0C) / R

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

A) R

B) XL

C) XC

D) Zero

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

A) Henry (H)

B) Ohm (Ω)

C) Farad (F)

D) Volt (V)

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

A) Ohm (Ω)

B) Farad (F)

C) Henry (H)

D) Watt (W)

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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)

44. 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

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

A) Angular frequency

B) Frequency

C) Wavelength

D) Amplitude

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

A) XC = 1 / (ωC)

B) XC = R

C) XC = ωL

D) XC = Z

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

A) Resistor

B) Capacitor

C) Inductor

D) Transformer

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

A) XL = 1 / (ωC)

B) XL = R

C) XL = ωL

D) XL = Z

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

A) Resistor

B) Capacitor

C) Inductor

D) Diode

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

A) Henry (H)

B) Farad (F)

C) Ohm (Ω)

D) Siemens (S)

Reactance, impedance and LCR series resonance - Question Bank