AC through Capacitor Capacitive Reactance - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: AC through Capacitor Capacitive Reactance
AC THROUGH CAPACITOR CAPACITIVE REACTANCE - UNSOLVED PRACTICE SET
Topic: AC through Capacitor Capacitive Reactance
Multiple Choice Questions
Q1. In a purely capacitive AC circuit, the current:
- Lags behind the voltage by 90ยฐ
- Leads the voltage by 90ยฐ
- Is in phase with the voltage
- Lags behind the voltage by 45ยฐ
Q2. The capacitive reactance (X_C) of a capacitor is given by:
- X_C = ฯC
- X_C = 1/(ฯC)
- X_C = C/ฯ
- X_C = ฯ/C
Q3. The SI unit of capacitive reactance is:
- Farad
- Henry
- Ohm
- Coulomb
Q4. In a purely capacitive circuit, the average power consumed over one complete cycle is:
- V_rms ร I_rms
- V_rmsยฒ / X_C
- Zero
- I_rmsยฒ ร X_C
Q5. If the frequency of an AC source connected to a pure capacitor is doubled, the capacitive reactance:
- Remains the same
- Doubles
- Becomes half
- Becomes four times
Q6. A capacitor blocks DC but allows AC to pass because:
- DC has infinite frequency
- Capacitive reactance is infinite for DC (f = 0) and finite for AC
- Capacitors store DC voltage
- AC has higher voltage than DC
Short Answer Questions
Q7. Define capacitive reactance. Write its expression and SI unit.
Q8. In a purely capacitive AC circuit, why is the average power consumed zero? Explain with reference to energy storage in the capacitor.
Q9. A capacitor of 10 ฮผF is connected to a 220 V, 50 Hz AC source. Calculate its capacitive reactance.
Q10. Why does a capacitor offer less opposition to AC of higher frequency? Explain the physical reason.
Q11. Draw the phasor diagram for a purely capacitive AC circuit. Show the phase relationship between voltage and current.
Q12. What happens to the brightness of a bulb connected in series with a capacitor when a dielectric slab is inserted between the plates of the capacitor? Explain.
Long Answer Questions
Q13. Derive the expression for the current in a purely capacitive AC circuit when the applied voltage is V = Vโ sin(ฯt). Show that the current leads the voltage by ฯ/2.
Q14. Explain why a capacitor blocks DC but allows AC to pass through. What is the physical basis of capacitive reactance and how does it vary with frequency?
Q15. A pure capacitor 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 the energy exchange between the capacitor and the source.
Numerical & Application-Based Problems
Q16. A capacitor of capacitance 50 ฮผF is connected to an AC source given by V = 200 sin(100ฯt) volts.
(a) Calculate the capacitive reactance of the capacitor.
(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 electric field of the capacitor.
Q17. A capacitor is connected to a 220 V, 50 Hz AC supply. The current in the circuit is measured to be 0.5 A.
(a) Calculate the capacitive reactance of the capacitor.
(b) Determine the capacitance of the capacitor.
(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 increases when frequency increases.
Q18. In your school's electronics club, a student is building a simple AC circuit for a project. She uses a 20 ฮผF capacitor and connects it across a variable frequency AC source of constant voltage 110 V.
(a) Calculate the current in the circuit when the frequency is 50 Hz.
(b) At what frequency will the current be twice the value calculated in part (a)?
(c) The student replaces the capacitor with a resistor of the same reactance value (at 50 Hz). Compare the phase relationship between voltage and current in both cases.
(d) Capacitors are often used in fan regulators in Indian homes. Explain how changing the capacitance affects the fan speed.