Resonance in LCR Circuit - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: Resonance in LCR Circuit
RESONANCE IN LCR CIRCUIT - UNSOLVED PRACTICE SET
Topic: Resonance in LCR Circuit
Multiple Choice Questions
Q1. In a series LCR circuit, resonance occurs when:
- X_L = 0
- X_C = 0
- X_L = X_C
- R = 0
Q2. At resonance in a series LCR circuit, the impedance is:
- Maximum and equal to X_L + X_C
- Minimum and equal to R
- Zero
- Infinite
Q3. The resonant frequency (fโ) of a series LCR circuit is given by:
- fโ = 1/(2ฯโLC)
- fโ = 2ฯโLC
- fโ = 1/(โLC)
- fโ = 2ฯLC
Q4. At resonance in a series LCR circuit, the current:
- Is minimum
- Is maximum and in phase with the voltage
- Leads the voltage by 90ยฐ
- Lags behind the voltage by 90ยฐ
Q5. The Q-factor of a series resonant circuit is a measure of:
- Its resistance
- Its sharpness of resonance
- Its power consumption
- Its impedance at resonance
Q6. In a series LCR circuit, if the resistance is increased, the resonance curve becomes:
- Sharper
- Flatter
- Unchanged
- Disappears
Short Answer Questions
Q7. Define electrical resonance in a series LCR circuit. What are the conditions for resonance?
Q8. What is the Q-factor of a resonant circuit? Write its expression for a series LCR circuit.
Q9. Why is the current maximum at resonance in a series LCR circuit? Explain.
Q10. At resonance, the voltage across the inductor can be many times the applied voltage. Does this violate the principle of conservation of energy? Explain.
Q11. Sketch the resonance curve (current vs frequency) for a series LCR circuit. Label the resonant frequency and half-power points.
Q12. How does the bandwidth of a resonant circuit relate to its Q-factor? What does a high Q-factor indicate?
Long Answer Questions
Q13. Derive the expression for the resonant frequency of a series LCR circuit. Show that at resonance, the current is maximum and is in phase with the applied voltage.
Q14. Explain the phenomenon of sharpness of resonance. Define Q-factor and derive its expression in terms of L, C, and R. How does Q-factor affect the selectivity of a radio receiver?
Q15. Draw the resonance curves for a series LCR circuit with different values of resistance (Rโ < Rโ < Rโ). Explain how the shape of the curve changes with resistance and discuss the practical significance.
Numerical & Application-Based Problems
Q16. A series LCR circuit consists of R = 20 ฮฉ, L = 0.5 H, and C = 20 ฮผF, connected to a variable frequency AC source of 100 V.
(a) Calculate the resonant frequency of the circuit.
(b) Find the current at resonance.
(c) Calculate the voltage across the inductor and capacitor at resonance.
(d) Determine the Q-factor of the circuit.
Q17. A series LCR circuit with L = 0.2 H, C = 50 ฮผF, and R = 10 ฮฉ is connected to a 200 V AC source.
(a) Find the resonant angular frequency.
(b) Calculate the maximum current in the circuit.
(c) Determine the bandwidth of the circuit.
(d) At what frequencies will the current drop to 1/โ2 times the maximum current?
Q18. In your school's science fair, a student builds a simple radio tuner using a variable capacitor (range 50 pF to 500 pF) and a fixed inductor of 2 mH.
(a) Calculate the range of frequencies that can be tuned by varying the capacitor.
(b) If the student wants to receive a radio station broadcasting at 1 MHz, what should be the capacitance setting?
(c) The circuit has a resistance of 5 ฮฉ. Calculate the Q-factor at 1 MHz and explain what it means for the selectivity of the radio.
(d) A classmate suggests using a higher resistance to 'protect' the circuit. Discuss whether this is a good idea for radio tuning purposes.