Resonance in RLC Circuits: Series vs Parallel Quiz Quiz

Challenge your understanding of resonance in series and parallel RLC circuits, including concepts like resonance frequency, impedance, and quality factor. This quiz covers essential topics for mastering the behavior and differences between these circuit types in practical electronics.

1. Identifying Resonance Frequency in a Series RLC Circuit

   In a series RLC circuit with R = 10 Ω, L = 100 mH, and C = 10 μF, what is the approximate resonance frequency (in Hz)?

   1. 1000 Hz
   2. 50 Hz
   3. 159 Hz
   4. 318 Hz

   Explanation: The resonance frequency is calculated using the formula fr = 1/(2π√(LC)), which gives approximately 159 Hz for the given values. 318 Hz and 1000 Hz are too high for these component values, and 50 Hz is too low and does not match the correct calculation. Only 159 Hz aligns with the mathematical solution for resonance frequency in a series RLC circuit.

2. Impedance at Resonance: Series vs Parallel

   Which best describes the total impedance of a series RLC circuit at resonance compared to that of a parallel RLC circuit at resonance?

   1. Series circuit impedance is minimum, parallel circuit impedance is maximum
   2. Both have minimum impedance at resonance
   3. Series circuit impedance is maximum, parallel circuit impedance is minimum
   4. Both have maximum impedance at resonance

   Explanation: At resonance, a series RLC circuit has its lowest impedance, equal to the resistance alone, while a parallel RLC circuit's impedance reaches a maximum. The second option reverses the situations, making it incorrect. The last two options incorrectly suggest identical behaviors for both types at resonance, which is not the case.

3. Current at Resonance in a Series RLC Circuit

   When an alternating voltage is applied to a series RLC circuit at resonance, what happens to the current in the circuit?

   1. It becomes minimum due to high reactance
   2. It drops to zero
   3. It becomes maximum due to minimal impedance
   4. It is unaffected by resonance

   Explanation: At resonance, the reactances cancel each other, leaving only the resistance, minimizing impedance and maximizing current. The second and third options are incorrect because current does not drop to zero or become minimum at resonance; rather, it increases. The fourth option wrongly claims resonance has no effect, ignoring fundamental circuit behavior.

4. Quality Factor Comparison

   For two identical RLC circuits, one in series and one in parallel, which statement best describes the quality factor (Q) at resonance, assuming equal component values?

   1. Both circuits have Q factors independent of resistance
   2. Series circuit Q = (1/R)√(L/C), parallel circuit Q = R√(C/L)
   3. Series circuit Q = R√(L/C), parallel circuit Q = (1/R)√(C/L)
   4. Series circuit Q = (1/R)√(C/L), parallel circuit Q = (1/R)√(L/C)

   Explanation: For a series RLC circuit, Q is (1/R) times the square root of L over C, and for the parallel case, Q equals R times the square root of C over L. The other equations either reverse L and C, or the role of R, leading to incorrect expressions. The last option wrongly states that the Q factor does not depend on resistance, which is not accurate.

5. Phase Relationship at Resonance

   At the resonant frequency in a series RLC circuit, what is the phase relationship between the source voltage and the circuit current?

   1. The voltage is always zero
   2. The current lags the voltage by 90 degrees
   3. The current is in phase with the voltage
   4. The current leads the voltage by 180 degrees

   Explanation: At resonance, the inductive and capacitive reactances cancel, so the current and voltage are in phase. The other options are incorrect: a 90-degree phase difference only occurs in purely reactive circuits, leading by 180 degrees is not physically meaningful for RLC resonance, and the voltage is not zero at resonance.