AC through Inductor Inductive Reactance - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: AC through Inductor Inductive Reactance
AC THROUGH INDUCTOR INDUCTIVE REACTANCE - UNSOLVED PRACTICE SET
Topic: AC through Inductor Inductive Reactance
Multiple Choice Questions
Q1. In a purely inductive AC circuit, the current:
- Leads the voltage by 90ยฐ
- Lags behind the voltage by 90ยฐ
- Is in phase with the voltage
- Leads the voltage by 45ยฐ
Q2. The inductive reactance (X_L) of an inductor is given by:
- X_L = 1/(ฯL)
- X_L = ฯL
- X_L = L/ฯ
- X_L = ฯ/L
Q3. The SI unit of inductive reactance is:
- Henry
- Ohm
- Farad
- Weber
Q4. In a purely inductive circuit, the average power consumed over one complete cycle is:
- V_rms ร I_rms
- V_rms ร I_rms / 2
- Zero
- V_rmsยฒ / X_L
Q5. If the frequency of an AC source connected to a pure inductor is doubled, the inductive reactance:
- Remains the same
- Becomes half
- Doubles
- Becomes four times
Q6. An ideal inductor in an AC circuit:
- Dissipates energy as heat
- Stores energy in its electric field
- Stores energy in its magnetic field
- Converts AC to DC
Short Answer Questions
Q7. Define inductive reactance. On what factors does it depend?
Q8. In a purely inductive AC circuit, why is the average power consumed zero? Explain with reference to the phase relationship between voltage and current.
Q9. An inductor of 0.5 H is connected to a 220 V, 50 Hz AC source. Calculate its inductive reactance.
Q10. Why does an inductor oppose the flow of alternating current? Explain the physical reason behind this opposition.
Q11. Draw the phasor diagram for a purely inductive AC circuit. Show the phase relationship between voltage and current.
Q12. What happens to the brightness of a bulb connected in series with an inductor when an iron rod is inserted inside the inductor? Explain.
Long Answer Questions
Q13. Derive the expression for the current in a purely inductive AC circuit when the applied voltage is V = Vโ sin(ฯt). Show that the current lags behind the voltage by ฯ/2.
Q14. Explain the physical basis of inductive reactance. Why does X_L increase with frequency? What would happen if a DC voltage were applied across an ideal inductor?
Q15. A pure inductor is connected to an AC source. Derive the expression for instantaneous power and show that the average power over a complete cycle is zero. Explain where the energy goes during different parts of the cycle.
Numerical & Application-Based Problems
Q16. A pure inductor of inductance 0.2 H is connected to an AC source given by V = 200 sin(100ฯt) volts.
(a) Calculate the inductive reactance of the inductor.
(b) Find the RMS value of the current in the circuit.
(c) Write the expression for the instantaneous current.
(d) Calculate the maximum energy stored in the magnetic field of the inductor.
Q17. An inductor is connected to a 220 V, 50 Hz AC supply. The current in the circuit is measured to be 2.2 A.
(a) Calculate the inductive reactance of the inductor.
(b) Determine the inductance of the inductor.
(c) If the frequency of the AC source is changed to 100 Hz while keeping the voltage constant, what will be the new current?
(d) Explain why the current decreases when frequency increases.
Q18. In your school's physics lab, a student builds a choke coil using 500 turns of copper wire wound around a hollow cardboard cylinder of length 25 cm and cross-sectional area 4 cmยฒ.
(a) Calculate the inductance of this air-cored solenoid.
(b) This choke is connected in series with a 60 W, 220 V bulb across a 220 V, 50 Hz AC supply. Calculate the current in the circuit and the voltage across the bulb.
(c) The student then inserts a soft iron rod inside the solenoid. Predict what happens to the bulb's brightness and explain why.
(d) Choke coils are used in tube lights instead of resistors to reduce current. Discuss one advantage of using a choke over a resistor for this purpose.