Electromagnetic Oscillations and Alternating Current Problems

This section provides 100 problems to test your understanding of electromagnetic oscillations and alternating current (AC) circuits, including calculations of oscillation frequency, impedance, resonance, and power in AC circuits. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering electromagnetism, a key topic for JEE/NEET success.

Numerical Problems

1. An LC circuit has $L = 0.1 , \text{H}$ and $C = 100 , \mu\text{F}$. Calculate the oscillation frequency $f$.

   • (a) $15.91 , \text{Hz}$
   • (b) $15.92 , \text{Hz}$
   • (c) $15.93 , \text{Hz}$
   • (d) $15.94 , \text{Hz}$

2. An LC circuit has $Q_0 = 20 , \mu\text{C}$, $L = 0.2 , \text{H}$, $C = 200 , \mu\text{F}$. Calculate the maximum current $I_0$.

   • (a) $9.99 \times 10^{-4} , \text{A}$
   • (b) $1.00 \times 10^{-3} , \text{A}$
   • (c) $1.01 \times 10^{-3} , \text{A}$
   • (d) $1.02 \times 10^{-3} , \text{A}$

3. An LC circuit has $L = 0.5 , \text{H}$, $C = 500 , \mu\text{F}$, $Q_0 = 10 , \mu\text{C}$. Calculate the total energy stored.

   • (a) $9.99 \times 10^{-8} , \text{J}$
   • (b) $1.00 \times 10^{-7} , \text{J}$
   • (c) $1.01 \times 10^{-7} , \text{J}$
   • (d) $1.02 \times 10^{-7} , \text{J}$

4. An AC circuit with $R = 50 , \Omega$ has $V_0 = 200 , \text{V}$. Calculate the peak current $I_0$.

   • (a) $3.99 , \text{A}$
   • (b) $4.00 , \text{A}$
   • (c) $4.01 , \text{A}$
   • (d) $4.02 , \text{A}$

5. A capacitor in an AC circuit has $C = 100 , \mu\text{F}$, $\omega = 200 , \text{rad/s}$, $I_0 = 2 , \text{A}$. Calculate the peak voltage $V_0$ across the capacitor.

   • (a) $49.9 , \text{V}$
   • (b) $50.0 , \text{V}$
   • (c) $50.1 , \text{V}$
   • (d) $50.2 , \text{V}$

6. An RL circuit has $R = 30 , \Omega$, $L = 0.15 , \text{H}$, $\omega = 400 , \text{rad/s}$, $V_0 = 120 , \text{V}$. Calculate the impedance $Z$.

   • (a) $67.0 , \Omega$
   • (b) $67.1 , \Omega$
   • (c) $67.2 , \Omega$
   • (d) $67.3 , \Omega$

7. A series RLC circuit has $R = 20 , \Omega$, $L = 0.1 , \text{H}$, $C = 100 , \mu\text{F}$, $\omega = 50 , \text{rad/s}$. Calculate the impedance $Z$.

   • (a) $103.8 , \Omega$
   • (b) $103.9 , \Omega$
   • (c) $104.0 , \Omega$
   • (d) $104.1 , \Omega$

8. An LC circuit has $L = 0.2 , \text{H}$, $C = 200 , \mu\text{F}$. Calculate the resonance frequency $\omega_0$.

   • (a) $49.9 , \text{rad/s}$
   • (b) $50.0 , \text{rad/s}$
   • (c) $50.1 , \text{rad/s}$
   • (d) $50.2 , \text{rad/s}$

9. An RLC circuit at resonance has $R = 40 , \Omega$, $V_0 = 80 , \text{V}$. Calculate $I_0$.

   • (a) $1.99 , \text{A}$
   • (b) $2.00 , \text{A}$
   • (c) $2.01 , \text{A}$
   • (d) $2.02 , \text{A}$

10. An AC circuit has $V_{\text{rms}} = 110 , \text{V}$, $I_{\text{rms}} = 3 , \text{A}$, power factor $\cos \phi = 0.8$. Calculate the average power $P_{\text{avg}}$.

    • (a) $263.9 , \text{W}$
    • (b) $264.0 , \text{W}$
    • (c) $264.1 , \text{W}$
    • (d) $264.2 , \text{W}$

11. An LC circuit has $L = 0.4 , \text{H}$, $C = 400 , \mu\text{F}$. Calculate the time period $T$.

    • (a) $0.250 , \text{s}$
    • (b) $0.251 , \text{s}$
    • (c) $0.252 , \text{s}$
    • (d) $0.253 , \text{s}$

12. An LC circuit has $Q_0 = 15 , \mu\text{C}$, $L = 0.3 , \text{H}$, $C = 300 , \mu\text{F}$. Calculate $I_0$.

    • (a) $5.99 \times 10^{-4} , \text{A}$
    • (b) $6.00 \times 10^{-4} , \text{A}$
    • (c) $6.01 \times 10^{-4} , \text{A}$
    • (d) $6.02 \times 10^{-4} , \text{A}$

13. An AC circuit with $R = 100 , \Omega$ has $V_{\text{rms}} = 220 , \text{V}$. Calculate $I_{\text{rms}}$.

    • (a) $2.19 , \text{A}$
    • (b) $2.20 , \text{A}$
    • (c) $2.21 , \text{A}$
    • (d) $2.22 , \text{A}$

14. An inductor in an AC circuit has $L = 0.2 , \text{H}$, $\omega = 300 , \text{rad/s}$, $I_0 = 1 , \text{A}$. Calculate $V_0$ across the inductor.

    • (a) $59.9 , \text{V}$
    • (b) $60.0 , \text{V}$
    • (c) $60.1 , \text{V}$
    • (d) $60.2 , \text{V}$

15. A series RLC circuit has $R = 10 , \Omega$, $L = 0.2 , \text{H}$, $C = 200 , \mu\text{F}$, $\omega = 100 , \text{rad/s}$. Calculate $Z$.

    • (a) $43.5 , \Omega$
    • (b) $43.6 , \Omega$
    • (c) $43.7 , \Omega$
    • (d) $43.8 , \Omega$

16. An RLC circuit has $L = 0.5 , \text{H}$, $C = 500 , \mu\text{F}$. Calculate $\omega_0$.

    • (a) $39.9 , \text{rad/s}$
    • (b) $40.0 , \text{rad/s}$
    • (c) $40.1 , \text{rad/s}$
    • (d) $40.2 , \text{rad/s}$

17. An AC circuit has $V_0 = 150 , \text{V}$, $I_0 = 3 , \text{A}$, $\cos \phi = 0.6$. Calculate $P_{\text{avg}}$.

    • (a) $134.9 , \text{W}$
    • (b) $135.0 , \text{W}$
    • (c) $135.1 , \text{W}$
    • (d) $135.2 , \text{W}$

18. A capacitor $C = 50 , \mu\text{F}$, $\omega = 400 , \text{rad/s}$, $V_0 = 100 , \text{V}$. Calculate $I_0$.

    • (a) $1.99 , \text{A}$
    • (b) $2.00 , \text{A}$
    • (c) $2.01 , \text{A}$
    • (d) $2.02 , \text{A}$

19. An RL circuit $R = 40 , \Omega$, $L = 0.1 , \text{H}$, $\omega = 500 , \text{rad/s}$, $V_0 = 80 , \text{V}$. Calculate $I_0$.

    • (a) $0.894 , \text{A}$
    • (b) $0.895 , \text{A}$
    • (c) $0.896 , \text{A}$
    • (d) $0.897 , \text{A}$

20. An LC circuit $L = 0.3 , \text{H}$, $C = 300 , \mu\text{F}$. Calculate $f$.

    • (a) $10.58 , \text{Hz}$
    • (b) $10.59 , \text{Hz}$
    • (c) $10.60 , \text{Hz}$
    • (d) $10.61 , \text{Hz}$

21. An LC circuit $Q_0 = 30 , \mu\text{C}$, $L = 0.4 , \text{H}$, $C = 400 , \mu\text{F}$. Calculate $U$.

    • (a) $1.12 \times 10^{-6} , \text{J}$
    • (b) $1.13 \times 10^{-6} , \text{J}$
    • (c) $1.14 \times 10^{-6} , \text{J}$
    • (d) $1.15 \times 10^{-6} , \text{J}$

22. An AC circuit $R = 25 , \Omega$, $V_0 = 50 , \text{V}$. Calculate $P_{\text{avg}}$.

    • (a) $49.9 , \text{W}$
    • (b) $50.0 , \text{W}$
    • (c) $50.1 , \text{W}$
    • (d) $50.2 , \text{W}$

23. An inductor $L = 0.3 , \text{H}$, $\omega = 200 , \text{rad/s}$, $V_0 = 60 , \text{V}$. Calculate $I_0$.

    • (a) $0.999 , \text{A}$
    • (b) $1.000 , \text{A}$
    • (c) $1.001 , \text{A}$
    • (d) $1.002 , \text{A}$

24. A series RLC circuit $R = 15 , \Omega$, $L = 0.05 , \text{H}$, $C = 50 , \mu\text{F}$, $\omega = 200 , \text{rad/s}$. Calculate $Z$.

    • (a) $52.2 , \Omega$
    • (b) $52.3 , \Omega$
    • (c) $52.4 , \Omega$
    • (d) $52.5 , \Omega$

25. An RLC circuit $L = 0.1 , \text{H}$, $C = 100 , \mu\text{F}$, $R = 20 , \Omega$, $V_0 = 60 , \text{V}$ at resonance. Calculate $I_0$.

    • (a) $2.99 , \text{A}$
    • (b) $3.00 , \text{A}$
    • (c) $3.01 , \text{A}$
    • (d) $3.02 , \text{A}$

26. An AC circuit $V_{\text{rms}} = 230 , \text{V}$, $I_{\text{rms}} = 2 , \text{A}$, $\cos \phi = 0.9$. Calculate $P_{\text{avg}}$.

    • (a) $413.9 , \text{W}$
    • (b) $414.0 , \text{W}$
    • (c) $414.1 , \text{W}$
    • (d) $414.2 , \text{W}$

27. A capacitor $C = 200 , \mu\text{F}$, $\omega = 100 , \text{rad/s}$, $I_0 = 4 , \text{A}$. Calculate $V_0$.

    • (a) $199.9 , \text{V}$
    • (b) $200.0 , \text{V}$
    • (c) $200.1 , \text{V}$
    • (d) $200.2 , \text{V}$

28. An RL circuit $R = 60 , \Omega$, $L = 0.2 , \text{H}$, $\omega = 300 , \text{rad/s}$. Calculate the phase angle $\phi$.

    • (a) $44.9^\circ$
    • (b) $45.0^\circ$
    • (c) $45.1^\circ$
    • (d) $45.2^\circ$

29. An LC circuit $L = 0.6 , \text{H}$, $C = 600 , \mu\text{F}$. Calculate $\omega_0$.

    • (a) $39.9 , \text{rad/s}$
    • (b) $40.0 , \text{rad/s}$
    • (c) $40.1 , \text{rad/s}$
    • (d) $40.2 , \text{rad/s}$

30. An AC circuit $V_0 = 100 , \text{V}$, $I_0 = 2 , \text{A}$, $\cos \phi = 0.5$. Calculate $P_{\text{avg}}$.

    • (a) $49.9 , \text{W}$
    • (b) $50.0 , \text{W}$
    • (c) $50.1 , \text{W}$
    • (d) $50.2 , \text{W}$

31. A spacecraft AC circuit has $L = 0.1 , \text{H}$, $C = 100 , \mu\text{F}$. Calculate $f$ for signal timing optimization.

    • (a) $15.91 , \text{Hz}$
    • (b) $15.92 , \text{Hz}$
    • (c) $15.93 , \text{Hz}$
    • (d) $15.94 , \text{Hz}$

32. An RLC circuit $R = 50 , \Omega$, $L = 0.2 , \text{H}$, $C = 200 , \mu\text{F}$, $V_0 = 150 , \text{V}$ at resonance. Calculate $I_0$.

    • (a) $2.99 , \text{A}$
    • (b) $3.00 , \text{A}$
    • (c) $3.01 , \text{A}$
    • (d) $3.02 , \text{A}$

33. An LC circuit $L = 0.8 , \text{H}$, $C = 800 , \mu\text{F}$. Calculate $T$.

    • (a) $0.223 , \text{s}$
    • (b) $0.224 , \text{s}$
    • (c) $0.225 , \text{s}$
    • (d) $0.226 , \text{s}$

34. An AC circuit $R = 75 , \Omega$, $V_{\text{rms}} = 150 , \text{V}$. Calculate $P_{\text{avg}}$.

    • (a) $299.9 , \text{W}$
    • (b) $300.0 , \text{W}$
    • (c) $300.1 , \text{W}$
    • (d) $300.2 , \text{W}$

35. An RL circuit $R = 20 , \Omega$, $L = 0.05 , \text{H}$, $\omega = 600 , \text{rad/s}$, $V_0 = 40 , \text{V}$. Calculate $I_0$.

    • (a) $0.632 , \text{A}$
    • (b) $0.633 , \text{A}$
    • (c) $0.634 , \text{A}$
    • (d) $0.635 , \text{A}$

Conceptual Problems

36. What is the oscillation frequency of an LC circuit proportional to?

• (a) $\sqrt{L C}$
• (b) $\frac{1}{\sqrt{L C}}$
• (c) $L C$
• (d) $\frac{1}{L C}$

37. What does a phasor represent in an AC circuit?

• (a) Instantaneous voltage
• (b) Sinusoidal voltage or current as a rotating vector
• (c) Average power
• (d) Resistance

38. What is the unit of impedance in SI units?

• (a) Ohm
• (b) Henry
• (c) Farad
• (d) Watt

39. What happens to the current in an RLC circuit at resonance?

• (a) Becomes zero
• (b) Becomes maximum
• (c) Becomes minimum
• (d) Oscillates randomly

40. What does the power factor $\cos \phi$ represent in an AC circuit?

• (a) Ratio of average power to apparent power
• (b) Ratio of resistance to reactance
• (c) Frequency of oscillation
• (d) Voltage amplitude

41. What is the unit of angular frequency $\omega$ in an LC circuit?

• (a) Hertz
• (b) Radians per second
• (c) Seconds
• (d) Joules

42. What does the inductive reactance $X_L$ depend on?

• (a) Resistance only
• (b) Frequency and inductance
• (c) Capacitance only
• (d) Voltage only

43. What happens to the impedance of an RLC circuit at resonance?

• (a) Becomes infinite
• (b) Equals the resistance $R$
• (c) Becomes zero
• (d) Depends on frequency

44. What does a power factor of 1 indicate in an AC circuit?

• (a) Purely reactive circuit
• (b) Purely resistive circuit
• (c) No power consumption
• (d) Maximum reactance

45. What is the dimension of impedance $Z$?

• (a) $[\text{M} \text{L}^2 \text{T}^{-3} \text{A}^{-2}]$
• (b) $[\text{M} \text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$

46. What does a zero average power in an AC circuit indicate?

• (a) Purely resistive circuit
• (b) Purely reactive circuit
• (c) No voltage
• (d) No current

47. What is the significance of $\frac{1}{\sqrt{L C}}$?

• (a) Impedance of an RLC circuit
• (b) Resonance frequency of an LC circuit
• (c) Power factor
• (d) Average power

48. What happens to the current in an LC circuit over time?

• (a) Grows exponentially
• (b) Decays exponentially
• (c) Oscillates sinusoidally
• (d) Remains constant

49. What does the phase difference between voltage and current in a capacitor indicate?

• (a) Voltage leads by $90^\circ$
• (b) Current leads by $90^\circ$
• (c) In phase
• (d) Out of phase by $180^\circ$

50. How do AC circuits function in spacecraft communication systems?

• (a) Increase resistance
• (b) Use resonance for signal tuning
• (c) Reduce frequency
• (d) Increase capacitance

Derivation Problems

51. Derive the oscillation frequency of an LC circuit $\omega = \frac{1}{\sqrt{L C}}$.

52. Derive the maximum current in an LC circuit $I_0 = \omega Q_0$.

53. Derive the total energy in an LC circuit $U = \frac{Q_0^2}{2C}$.

54. Derive the impedance of a series RLC circuit $Z = \sqrt{R^2 + (X_L - X_C)^2}$.

55. Derive the resonance frequency of an RLC circuit $\omega_0 = \frac{1}{\sqrt{L C}}$.

56. Derive the average power in an AC circuit $P_{\text{avg}} = \frac{V_0 I_0}{2} \cos \phi$.

57. Derive the power factor $\cos \phi$ in an RL circuit $\cos \phi = \frac{R}{Z}$.

58. Derive the phase angle in an RLC circuit $\tan \phi = \frac{X_L - X_C}{R}$.

59. Derive the inductive reactance $X_L = \omega L$.

60. Derive the capacitive reactance $X_C = \frac{1}{\omega C}$.

61. Derive the rms voltage $V_{\text{rms}} = \frac{V_0}{\sqrt{2}}$ in an AC circuit.

62. Derive the current oscillation in an LC circuit $I = -\omega Q_0 \sin (\omega t + \phi)$.

63. Derive the voltage across a capacitor in an AC circuit $V_C = I X_C$.

64. Derive the condition for maximum current in an RLC circuit at resonance.

65. Derive the energy oscillation between $L$ and $C$ in an LC circuit.

NEET-style Conceptual Problems

66. What is the unit of frequency in an LC circuit in SI units?

• (a) Hertz
• (b) Weber
• (c) Ohm
• (d) Volt

67. What does a sinusoidal voltage in an AC circuit indicate?

• (a) Constant voltage
• (b) Oscillating voltage with time
• (c) Zero voltage
• (d) Static voltage

68. What is the relationship between inductive reactance $X_L$ and frequency $\omega$?

• (a) $X_L \propto \frac{1}{\omega}$
• (b) $X_L \propto \omega$
• (c) $X_L$ is independent of $\omega$
• (d) $X_L \propto \omega^2$

69. What happens to the impedance in an RLC circuit at resonance?

• (a) Becomes maximum
• (b) Equals $R$
• (c) Becomes zero
• (d) Becomes infinite

70. What is the dimension of $X_L$?

• (a) $[\text{M} \text{L}^2 \text{T}^{-3} \text{A}^{-2}]$
• (b) $[\text{M} \text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$

71. What does the total energy in an LC circuit depend on?

• (a) Resistance
• (b) Maximum charge and capacitance
• (c) Frequency only
• (d) Voltage only

72. What is the role of phasors in AC circuit analysis?

• (a) Increase voltage
• (b) Simplify sinusoidal calculations
• (c) Reduce current
• (d) Increase resistance

73. What happens to the average power in a purely capacitive AC circuit?

• (a) Becomes maximum
• (b) Becomes zero
• (c) Equals $V_{\text{rms}} I_{\text{rms}}$
• (d) Becomes infinite

74. Why does the current peak at resonance in an RLC circuit?

• (a) Due to $X_L = X_C$
• (b) Due to increased resistance
• (c) Due to decreased frequency
• (d) Due to static voltage

75. What is the unit of average power in an AC circuit?

• (a) Watt
• (b) Volt
• (c) Ampere
• (d) Ohm

76. What does a constant current in an LC circuit indicate?

• (a) Oscillating charge
• (b) No oscillation
• (c) Maximum energy in $L$
• (d) Maximum energy in $C$

77. Which type of circuit exhibits resonance?

• (a) Pure resistive circuit
• (b) RL circuit
• (c) RLC circuit
• (d) RC circuit

78. What is the phase relationship in a purely inductive AC circuit?

• (a) Voltage lags by $90^\circ$
• (b) Voltage leads by $90^\circ$
• (c) In phase
• (d) Out of phase by $180^\circ$

79. What does a pseudo-force do in a non-inertial frame for AC circuit calculations?

• (a) Affects perceived voltage
• (b) Affects charge distribution
• (c) Creates oscillations
• (d) Reduces impedance

80. What is the dimension of $V_{\text{rms}} I_{\text{rms}}$?

• (a) $[\text{M} \text{L}^2 \text{T}^{-3}]$
• (b) $[\text{M} \text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$

81. What is the role of resonance in spacecraft communication systems?

• (a) Increases resistance
• (b) Optimizes signal frequency
• (c) Reduces voltage
• (d) Increases capacitance

82. What happens to the energy in an LC circuit over time?

• (a) Dissipates completely
• (b) Oscillates between $L$ and $C$
• (c) Remains constant in $L$
• (d) Remains constant in $C$

83. Why does the impedance in an RLC circuit depend on frequency?

• (a) Due to $X_L$ and $X_C$ varying with $\omega$
• (b) Due to increased resistance
• (c) Due to decreased capacitance
• (d) Due to static voltage

84. What is the significance of $\frac{V_0 I_0}{2} \cos \phi$?

• (a) Impedance in an RLC circuit
• (b) Average power in an AC circuit
• (c) Resonance frequency
• (d) Maximum current

85. What is the unit of reactance in an AC circuit?

• (a) Ohm
• (b) Volt
• (c) Ampere
• (d) Henry

86. What does a maximum current at resonance in an RLC circuit indicate?

• (a) $Z$ is maximum
• (b) $Z$ equals $R$
• (c) No oscillation
• (d) Infinite power

87. What is the physical significance of $\omega L$?

• (a) Capacitive reactance
• (b) Inductive reactance
• (c) Resonance frequency
• (d) Average power

88. Why does the average power in a purely resistive AC circuit equal $V_{\text{rms}} I_{\text{rms}}$?

• (a) Due to $\cos \phi = 1$
• (b) Due to $\cos \phi = 0$
• (c) Due to increased reactance
• (d) Due to decreased frequency

89. What is the dimension of $\frac{1}{\omega C}$?

• (a) $[\text{M} \text{L}^2 \text{T}^{-3} \text{A}^{-2}]$
• (b) $[\text{M} \text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$

90. How does the power factor affect spacecraft power systems?

• (a) Increases current
• (b) Optimizes power delivery efficiency
• (c) Reduces voltage
• (d) Increases resistance

91. What is the role of frequency in the capacitive reactance $X_C$?

• (a) $X_C \propto \omega$
• (b) $X_C \propto \frac{1}{\omega}$
• (c) No dependence
• (d) $X_C \propto \omega^2$

92. What does a high power factor in an AC circuit indicate?

• (a) High reactance
• (b) Efficient power delivery
• (c) No power consumption
• (d) Infinite current

93. What is the physical significance of $\sqrt{R^2 + (X_L - X_C)^2}$?

• (a) Resonance frequency
• (b) Impedance in an RLC circuit
• (c) Average power
• (d) Maximum voltage

94. What is the dimension of $\omega$ in an LC circuit?

• (a) $[\text{T}^{-1}]$
• (b) $[\text{M} \text{L} \text{T}^{-1}]$
• (c) $[\text{L} \text{T}^{-2}]$
• (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$

95. Why does the voltage across an inductor lead the current in an AC circuit?

• (a) Due to $V_L = I X_L$ and phase difference
• (b) Due to increased resistance
• (c) Due to decreased capacitance
• (d) Due to static voltage

NEET-style Numerical Problems

96. An LC circuit has $L = 0.2 , \text{H}$, $C = 200 , \mu\text{F}$. Calculate $f$.

• (a) $11.25 , \text{Hz}$
• (b) $11.26 , \text{Hz}$
• (c) $11.27 , \text{Hz}$
• (d) $11.28 , \text{Hz}$

97. An AC circuit $R = 60 , \Omega$, $V_0 = 120 , \text{V}$. Calculate $I_0$.

• (a) $1.99 , \text{A}$
• (b) $2.00 , \text{A}$
• (c) $2.01 , \text{A}$
• (d) $2.02 , \text{A}$

98. A series RLC circuit $R = 30 , \Omega$, $L = 0.1 , \text{H}$, $C = 100 , \mu\text{F}$, $\omega = 50 , \text{rad/s}$. Calculate $Z$.

• (a) $103.8 , \Omega$
• (b) $103.9 , \Omega$
• (c) $104.0 , \Omega$
• (d) $104.1 , \Omega$

99. An RLC circuit $L = 0.4 , \text{H}$, $C = 400 , \mu\text{F}$. Calculate $\omega_0$.

• (a) $49.9 , \text{rad/s}$
• (b) $50.0 , \text{rad/s}$
• (c) $50.1 , \text{rad/s}$
• (d) $50.2 , \text{rad/s}$

100. An AC circuit $V_{\text{rms}} = 120 , \text{V}$, $I_{\text{rms}} = 2 , \text{A}$, $\cos \phi = 0.7$. Calculate $P_{\text{avg}}$.
     - (a) $167.9 , \text{W}$
     - (b) $168.0 , \text{W}$
     - (c) $168.1 , \text{W}$
     - (d) $168.2 , \text{W}$

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