Rlc Circuits And Resonance MCQs with Explanations

Let's understand this concept step by step. A parallel resonant circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel. It resonates at a particular frequency called the resonant frequency . The bandwidth is the range of frequencies around the resonant frequency over which the circuit responds effectively. A narrow bandwidth indicates high selectivity, while a wide bandwidth indicates lower selectivity. The selectivity of a parallel resonant circuit is measured by its Quality Factor (Q-factor) . For a parallel resonant circuit, the Q-factor is directly proportional to the parallel resistance (R) . The relationship between bandwidth and Q-factor is: Bandwidth = Resonant Frequency / Q-factor This means that bandwidth is inversely proportional to the Q-factor . When the parallel resistance is reduced , the Q-factor decreases . As the Q-factor decreases, the bandwidth increases , making the resonance curve broader and the circuit less selective. Therefore, reducing the resistance in parallel with a parallel resonant circuit increases its bandwidth . Hence, the correct answer is Option C: Increases .

Quality factor (Q): The quality factor is a dimensionless parameter that represents the ratio of the energy stored in the circuit to the energy dissipated per cycle. Formula for Q: For a series RLC circuit, the quality factor is given by: Q = (1/R) × √(L/C) Here, R is the resistance, L is the inductance, and C is the capacitance. True power vs. Apparent power: The ratio of true power to apparent power is the power factor (cos φ), not the quality factor. Key distinction: The quality factor is related to the sharpness of resonance in a circuit, while the power factor represents the efficiency of power usage in an AC circuit. Thus, the statement that the quality factor (Q) is the ratio of true power to apparent power is false.

The bandwidth ( BW ) of a resonant circuit can be calculated using the formula: $$BW = \text{Upper Critical Frequency} - \text{Lower Critical Frequency}$$ In this case: Lower Critical Frequency ($$f_1$$) = 7 kHz Upper Critical Frequency ($$f_2$$) = 13 kHz Now, we can calculate the bandwidth: $$BW = f_2 - f_1 = 13 \, \text{kHz} - 7 \, \text{kHz} = 6 \, \text{kHz}$$ So, the bandwidth of the circuit is 6 kHz . The correct answer is Option A: 6 kHz .

True is the correct answer to “Resonance is a condition in a series RLC circuit in which the capacitive and inductive reactances are equal in magnitude.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

True is the correct answer to “If the value of C in a series RLC circuit is decreased, the resonant frequency increases”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

False is the correct answer to “A lower Q produces a narrower bandwidth.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

Decrease is the correct answer to “A certain series resonant circuit has a bandwidth of 2 kHz. If the existing coil is replaced with one having a higher value of Q, the bandwidth will”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

18,780 Ω is the correct answer to “A 6.8 kΩ resistor, a 7 mH coil, and a 0.02 µF capacitor are in parallel across a 17 kHz ac source. The coil's internal resistance, R W , is 30 Ω. The equivalent parallel resistance, R p (eq), is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

90 Ω is the correct answer to “The impedance at the resonant frequency of a series RLC circuit with L = 20 mH, C = 0.02 µF, and RW = 90 Ω is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

True is the correct answer to “In a parallel RLC circuit, the smaller reactance determines the net reactance of the circuit.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

True is the correct answer to “In a series RLC circuit, the larger reactance determines the net reactance of the circuit.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

Decreased is the correct answer to “To tune a parallel resonant circuit to a higher frequency, the capacitance should be”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

True is the correct answer to “The reactive voltages, V L and V C , cancel at resonance.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

12.7 Ω is the correct answer to “A 15 Ω resistor, an inductor with 8 Ω inductive reactance, and a capacitor with 12 Ω capacitive reactance are in parallel across an ac voltage source. The circuit impedance is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

17,340 Ω is the correct answer to “A 9 mH coil is in parallel with a 0.015 µF capacitor across an 18 kHz ac source. The coil's internal resistance R W , is 60 Ω. The circuit impedance is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

200 Ω is the correct answer to “A 200 Ω resistor, a coil with 30 Ω of reactance, and a capacitor of unknown reactance are in series across an ac source. The circuit is at resonance. Circuit impedance is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

Increases is the correct answer to “If the value of C in a series RLC circuit is decreased, the resonant frequency”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

12.28 ∠12.34° Ω is the correct answer to “A certain series RLC circuit with a 200 Hz, 15 V ac source has the following values: R = 12 Ω, C = 80 µF, and L = 10 mH. The total impedance, expressed in polar form, is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

Lags the applied voltage is the correct answer to “In a series RLC circuit that is operating above the resonant frequency, the current”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

281 Hz is the correct answer to “A 12 Ω resistor, a 40 µF capacitor, and an 8 mH coil are in series across an ac source. The resonant frequency is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

4,337 Ω is the correct answer to “A resistor of 3 kΩ, a 0.05 µF capacitor, and a 120 mH coil are in series across a 5 kHz, 20 V ac source. What is the impedance, expressed in polar form”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

40 V is the correct answer to “In a certain series resonant circuit, V C = 125 V, V L = 125 V, and V R = 40 V. The value of the source voltage is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

10,866 Hz is the correct answer to “A 15 Ω resistor, a 220 µH coil, and a 60 pF capacitor are in series across an ac source. What is the bandwidth of the circuit”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

False is the correct answer to “In a series RLC circuit, the current is minimum at resonance.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

False is the correct answer to “A series resonant circuit is commonly called a tank circuit.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

1,616 Ω is the correct answer to “A 10 Ω resistor, a 90 mH coil, and a 0.015 µF capacitor are in series across an ac source. The impedance magnitude at 1,200 Hz below f r is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

False is the correct answer to “At series resonance, the inductive reactance and capacitive reactance are never equal.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

130 mA is the correct answer to “A 90 Ω resistor, a coil with 30 Ω of reactance, and a capacitor with 50 Ω of reactance are in series across a 12 V ac source. The current through the resistor is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

300 V is the correct answer to “A 24 Ω resistor, an inductor with a reactance of 120 Ω, and a capacitor with a reactance of 120 Ω are in series across a 60 V source. The circuit is at resonance. The voltage across the inductor is”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.

True is the correct answer to “X L and X C have opposing effects in an RLC circuit.”. This question is standard in competitive examination syllabi for Rlc Circuits And Resonance.