AC through Resistor - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: AC through Resistor
AC THROUGH RESISTOR - UNSOLVED PRACTICE SET
Topic: AC through Resistor
Multiple Choice Questions
Q1. In a purely resistive AC circuit, the phase difference between voltage and current is:
- Ο/2 (90Β°)
- Ο (180Β°)
- Zero
- Ο/4 (45Β°)
Q2. The instantaneous power dissipated in a resistor in an AC circuit is given by:
- P = IΒ²R
- P = IβΒ²R sinΒ²(Οt)
- P = VβIβ sin(Οt)
- P = VβIβ cos(Οt)
Q3. In a purely resistive AC circuit, if the voltage is V = Vβ sin(Οt), the current is:
- I = Iβ cos(Οt)
- I = Iβ sin(Οt)
- I = Iβ sin(Οt + Ο/2)
- I = Iβ sin(Οt β Ο/2)
Q4. The average power dissipated in a resistor over one complete cycle of AC is:
- Zero
- VβIβ/2
- VβIβ
- VβIβ/β2
Q5. In a resistive AC circuit, the power factor is:
- Zero
- 0.5
- 1
- Infinity
Q6. When an AC voltage is applied across a resistor, the heat produced is:
- More than that produced by DC of the same RMS value
- Less than that produced by DC of the same RMS value
- Equal to that produced by DC of the same RMS value
- Zero
Short Answer Questions
Q7. Show that in a purely resistive AC circuit, the voltage and current are in the same phase. Draw the corresponding phasor diagram.
Q8. An AC voltage V = Vβ sin(Οt) is applied across a resistor R. Write the expression for instantaneous current and instantaneous power.
Q9. Why does a resistor in an AC circuit always dissipate power as heat, regardless of the direction of current?
Q10. A 100 Ξ© resistor is connected to a 220 V, 50 Hz AC supply. Calculate the RMS current flowing through it.
Q11. Draw the graphical representation of voltage, current, and power as functions of time in a purely resistive AC circuit.
Q12. Why is the average power in a resistive AC circuit never zero, even though the instantaneous power becomes negative during parts of the cycle?
Long Answer Questions
Q13. Derive the expression for instantaneous power in a purely resistive AC circuit. Show graphically how the power varies with time and prove that the average power is P_avg = V_rms Γ I_rms.
Q14. A resistor R is connected to an AC source V = Vβ sin(Οt). Derive the expression for the current and show that it is in phase with the voltage. Draw the voltage-current graphs.
Q15. Explain why the heating effect of an alternating current in a resistor is the same as that of a direct current of the same RMS value. Use this to justify why household appliances are rated in terms of RMS voltage.
Numerical & Application-Based Problems
Q16. A 50 Ξ© resistor is connected to an AC source given by V = 200 sin(100Οt) volts.
(a) Write the expression for the instantaneous current in the circuit.
(b) Calculate the RMS values of voltage and current.
(c) Find the average power dissipated in the resistor.
(d) Determine the frequency of the AC supply.
Q17. An electric bulb is rated 100 W, 220 V AC. It is connected to a 220 V, 50 Hz AC mains.
(a) Calculate the resistance of the bulb.
(b) Find the peak current flowing through the bulb.
(c) Write the equation for instantaneous current through the bulb.
(d) Calculate the energy consumed by the bulb in 5 hours.
Q18. In your school's physics lab, a student sets up an experiment with a 40 Ξ© resistor connected to a variable AC source. When the source frequency is set to 50 Hz, the voltmeter reads 110 V and the ammeter reads 2.75 A.
(a) Verify whether the readings are consistent with Ohm's law for AC circuits.
(b) Calculate the peak voltage of the AC source.
(c) The student then replaces the resistor with another resistor and observes that at the same voltage, the current becomes half. Find the new resistance.
(d) Explain why the frequency of the AC source does not affect the current in a purely resistive circuit.