LR CR and LCR Series Circuit - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: LR CR and LCR Series Circuit
LR CR AND LCR SERIES CIRCUIT - UNSOLVED PRACTICE SET
Topic: LR CR and LCR Series Circuit
Multiple Choice Questions
Q1. In a series LCR circuit, the impedance Z is given by:
- Z = √[R² + (X_L + X_C)²]
- Z = √[R² + (X_L − X_C)²]
- Z = R + X_L + X_C
- Z = √[R² + X_L² + X_C²]
Q2. In a series LR circuit, the phase angle φ by which voltage leads the current is given by:
- tan φ = X_L/R
- tan φ = R/X_L
- tan φ = X_C/R
- tan φ = R/X_C
Q3. In a series CR circuit, the current:
- Leads the voltage
- Lags behind the voltage
- Is in phase with the voltage
- Is independent of frequency
Q4. In a series LCR circuit at resonance:
- X_L = X_C and Z = R
- X_L = 2X_C and Z = 0
- X_L = X_C/2 and Z = ∞
- X_L + X_C = R
Q5. The voltage across the inductor in a series LCR circuit can be:
- Equal to the applied voltage
- Greater than the applied voltage
- Less than the applied voltage
- All of the above
Q6. In a series LCR circuit, if X_L > X_C, the circuit behaves as:
- Purely resistive
- Capacitive
- Inductive
- Resonant
Short Answer Questions
Q7. Write the expression for impedance in a series LCR circuit. Explain the significance of each term.
Q8. In a series LR circuit, derive the expression for the phase difference between voltage and current.
Q9. A series LCR circuit has R = 10 Ω, X_L = 20 Ω, and X_C = 10 Ω. Calculate the impedance of the circuit.
Q10. Why can the voltage across the inductor or capacitor in a series LCR circuit be greater than the applied voltage? Explain.
Q11. Draw the impedance triangle for a series LCR circuit and explain how it helps in calculating the phase angle.
Q12. What is meant by the term 'reactance' in an AC circuit? Distinguish between inductive reactance and capacitive reactance.
Long Answer Questions
Q13. Derive the expression for the current and impedance in a series LCR circuit when an AC voltage V = V₀ sin(ωt) is applied. Show the phase relationship using a phasor diagram.
Q14. Explain the behaviour of a series LCR circuit when:
(a) X_L > X_C
(b) X_L < X_C
(c) X_L = X_C
Draw the corresponding phasor diagrams for each case.
Q15. A resistor R, an inductor L, and a capacitor C are connected in series across an AC source. Show that the voltage across the combination is given by V = I√[R² + (X_L − X_C)²]. Explain why the voltages across L and C are 180° out of phase with each other.
Numerical & Application-Based Problems
Q16. A series LCR circuit consists of R = 40 Ω, L = 100 mH, and C = 50 μF, connected to a 200 V, 50 Hz AC supply.
(a) Calculate the inductive reactance, capacitive reactance, and impedance of the circuit.
(b) Find the current flowing through the circuit.
(c) Calculate the voltage across each component (R, L, and C).
(d) Determine the phase angle between the applied voltage and the current.
Q17. A coil having a resistance of 20 Ω and inductance of 0.2 H is connected in series with a capacitor of 30 μF across a 220 V variable frequency AC source.
(a) At what frequency will the circuit draw maximum current?
(b) Calculate the maximum current.
(c) Find the voltage across the inductor at resonance.
(d) What is the Q-factor of the circuit?
Q18. In your school's physics lab, a student sets up a series circuit with a 30 Ω resistor, a 0.5 H inductor, and a variable capacitor connected to a 220 V, 50 Hz AC supply. The student adjusts the capacitor until the current in the circuit is maximum.
(a) Calculate the value of capacitance at this condition.
(b) Determine the maximum current and the voltage across each component.
(c) The student then replaces the AC source with a 220 V DC source. Predict what happens to the current and explain why.
(d) Series LCR circuits are used in radio tuning. Explain how changing the capacitance allows you to select different radio stations.