set-2

Answer: 1. Equal and opposite

Explanation:

• At resonance, the voltage across the inductor ($V_L$) and the capacitor ($V_C$) are equal in magnitude but opposite in phase.
• Therefore, they cancel each other out, and the total voltage across the LC combination is zero.
• The correct answer is Equal and opposite.

Answer: 1. Unity

Explanation:

• At resonance, the impedance of the series R-L-C circuit is purely resistive ($Z = R$).
• The phase angle between voltage and current is zero, and the power factor is unity.
• Therefore, the correct answer is Unity.

Answer: 1. Minimum

Explanation:

• At resonance, the impedance of the series R-L-C circuit is minimum and equal to the resistance ($Z = R$).
• Therefore, the correct answer is Minimum.

Answer: 2. Inversely proportional to Q factor

Explanation:

• The bandwidth ($BW$) of a series R-L-C circuit is given by:
  $BW = \frac{f_r}{Q}$
  where:
  • $f_r$ = resonant frequency,
  • $Q$ = quality factor.
• Therefore, the bandwidth is inversely proportional to the Q factor.
• The correct answer is Inversely proportional to Q factor.

Answer: 1. Directly proportional to resonant frequency

Explanation:

• The quality factor ($Q$) of a series R-L-C circuit is given by:
  $Q = \frac{f_r}{BW}$
  where:
  • $f_r$ = resonant frequency,
  • $BW$ = bandwidth.
• Therefore, the quality factor is directly proportional to the resonant frequency.
• The correct answer is Directly proportional to resonant frequency.

Answer: 1. $\frac{1}{2\pi \sqrt{LC}}$

Explanation:

• The resonant frequency ($f_r$) of a series R-L-C circuit is given by:
  $f_r = \frac{1}{2\pi \sqrt{LC}}$
• Therefore, the correct answer is $\frac{1}{2\pi \sqrt{LC}}$.

Answer: 1. Minimum

Explanation:

• At resonance, the impedance of the parallel R-L-C circuit is maximum, and the current is minimum.
• Therefore, the correct answer is Minimum.

Answer: 2. Maximum

Explanation:

• At resonance, the impedance of the parallel R-L-C circuit is maximum.
• Therefore, the correct answer is Maximum.

Answer: 1. Unity

Explanation:

• At resonance, the impedance of the parallel R-L-C circuit is purely resistive ($Z = R$).
• The phase angle between voltage and current is zero, and the power factor is unity.
• Therefore, the correct answer is Unity.

Answer: 2. Inversely proportional to Q factor

Explanation:

• The bandwidth ($BW$) of a parallel R-L-C circuit is given by:
  $BW = \frac{f_r}{Q}$
  where:
  • $f_r$ = resonant frequency,
  • $Q$ = quality factor.
• Therefore, the bandwidth is inversely proportional to the Q factor.
• The correct answer is Inversely proportional to Q factor.

Answer: 1. Directly proportional to resonant frequency

Explanation:

• The quality factor ($Q$) of a parallel R-L-C circuit is given by:
  $Q = \frac{f_r}{BW}$
  where:
  • $f_r$ = resonant frequency,
  • $BW$ = bandwidth.
• Therefore, the quality factor is directly proportional to the resonant frequency.
• The correct answer is Directly proportional to resonant frequency.

Answer: 1. $\frac{1}{2\pi \sqrt{LC}}$

Explanation:

• The resonant frequency ($f_r$) of a parallel R-L-C circuit is given by:
  $f_r = \frac{1}{2\pi \sqrt{LC}}$
• Therefore, the correct answer is $\frac{1}{2\pi \sqrt{LC}}$.

Answer: 1. Equal to the applied voltage

Explanation:

• At resonance, the voltage across the inductor ($V_L$) and the capacitor ($V_C$) cancel each other out.
• The entire applied voltage appears across the resistor ($V_R$).
• Therefore, the correct answer is Equal to the applied voltage.

Answer: 1. Equal to the total current

Explanation:

• At resonance, the current through the inductor ($I_L$) and the capacitor ($I_C$) cancel each other out.
• The entire current flows through the resistor ($I_R$).
• Therefore, the correct answer is Equal to the total current.

Answer: 1. Q times the applied voltage

Explanation:

• At resonance, the voltage across the inductor ($V_L$) is given by:
  $V_L = Q \cdot V$
  where:
  • $Q$ = quality factor,
  • $V$ = applied voltage.
• Therefore, the correct answer is Q times the applied voltage.

Answer: 1. Q times the total current

Explanation:

• At resonance, the current through the inductor ($I_L$) is given by:
  $I_L = Q \cdot I$
  where:
  • $Q$ = quality factor,
  • $I$ = total current.
• Therefore, the correct answer is Q times the total current.

Answer: 1. Q times the applied voltage

Explanation:

• At resonance, the voltage across the capacitor ($V_C$) is given by:
  $V_C = Q \cdot V$
  where:
  • $Q$ = quality factor,
  • $V$ = applied voltage.
• Therefore, the correct answer is Q times the applied voltage.

Answer: 1. Q times the total current

Explanation:

• At resonance, the current through the capacitor ($I_C$) is given by:
  $I_C = Q \cdot I$
  where:
  • $Q$ = quality factor,
  • $I$ = total current.
• Therefore, the correct answer is Q times the total current.

Answer: 1. Maximum

Explanation:

• At resonance, the impedance of the series R-L-C circuit is minimum, and the current is maximum.
• Therefore, the power dissipated is maximum.
• The correct answer is Maximum.

Answer: 1. Minimum

Explanation:

• At resonance, the impedance of the parallel R-L-C circuit is maximum, and the current is minimum.
• Therefore, the power dissipated is minimum.
• The correct answer is Minimum.

Answer: 1. $X_L > X_C$

Explanation:

• In a series R-L-C circuit, the current lags the voltage when the inductive reactance ($X_L$) is greater than the capacitive reactance ($X_C$).
• Therefore, the correct answer is $X_L > X_C$.

Answer: 4. Infinite

Explanation:

• In a short circuit, the resistance is effectively zero, and the current becomes extremely high (theoretically infinite).
• Therefore, the correct answer is Infinite.

Answer: 4. All of the above

Explanation:

• The unit ohm (Ω) is used for:
  • Resistance ($R$),
  • Inductive reactance ($X_L$),
  • Capacitive reactance ($X_C$).
• Therefore, the correct answer is All of the above.

Answer: 3. Both A & B

Explanation:

• The unit siemens (S) or mho (℧) is used for:
  • Conductance ($G = \frac{1}{R}$),
  • Admittance ($Y = \frac{1}{Z}$).
• Therefore, the correct answer is Both A & B.

Answer: 3. Transistors

Explanation:

• Ohm’s law is applicable only to linear elements like resistors, capacitors, and inductors.
• Transistors are non-linear devices and cannot be analyzed using Ohm’s law.
• Therefore, the correct answer is Transistors.

Answer: 4. RMS value * Peak factor

Explanation:

• The peak value of an AC waveform is given by:
  $V_{peak} = V_{rms} \times \text{Peak factor}$
  where the peak factor for a sinusoidal waveform is $\sqrt{2}$.
• Therefore, the correct answer is RMS value * Peak factor.

Answer: 4. 200

Explanation:

• The number of cycles in a given time is calculated as:
  $\text{Number of cycles} = \text{Frequency} \times \text{Time}$
  $\text{Number of cycles} = 100 \, \text{Hz} \times 2 \, \text{s} = 200$
• Therefore, the correct answer is 200.

Answer: 3. Scalar quantity

Explanation:

• Electric potential is a scalar quantity because it has only magnitude and no direction.
• Therefore, the correct answer is Scalar quantity.

Answer: 1. RMS value / Form factor

Explanation:

• The average value of an AC waveform is given by:
  $V_{avg} = \frac{V_{rms}}{\text{Form factor}}$
  where the form factor for a sinusoidal waveform is approximately 1.11.
• Therefore, the correct answer is RMS value / Form factor.