Phasors and Phasor Diagrams - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: Phasors and Phasor Diagrams
PHASORS AND PHASOR DIAGRAMS - UNSOLVED PRACTICE SET
Topic: Phasors and Phasor Diagrams
Multiple Choice Questions
Q1. A phasor is a:
- Scalar quantity representing AC magnitude
- Rotating vector representing the amplitude and phase of an AC quantity
- Fixed vector in space
- Graph of voltage versus time
Q2. In a phasor diagram for a purely resistive AC circuit, the voltage and current phasors are:
- Perpendicular to each other
- In opposite directions
- Along the same direction
- At 45ยฐ to each other
Q3. In a phasor diagram for a series LCR circuit, the angle between the current phasor and the voltage phasor represents:
- The frequency of AC
- The phase difference between current and voltage
- The resistance of the circuit
- The power factor
Q4. The length of a phasor represents:
- The frequency of the AC quantity
- The RMS or peak value of the AC quantity
- The time period of the AC quantity
- The phase angle only
Q5. In a phasor diagram for a series LR circuit, the voltage phasor diagram forms a:
- Straight line
- Right-angled triangle
- Circle
- Parallelogram
Q6. The phasor representing current in a purely capacitive circuit is drawn:
- Along the positive x-axis
- Along the positive y-axis
- 90ยฐ ahead of the voltage phasor
- 90ยฐ behind the voltage phasor
Short Answer Questions
Q7. What is a phasor? Why are phasor diagrams useful in analyzing AC circuits?
Q8. Draw the phasor diagram for a purely inductive AC circuit, showing the phase relationship between voltage and current.
Q9. In a series CR circuit, draw the phasor diagram and indicate the phase angle. Is the current leading or lagging the voltage?
Q10. Explain why we cannot simply add the voltages across R, L, and C in a series LCR circuit algebraically. How does the phasor method solve this problem?
Q11. Draw the phasor diagram for a series LCR circuit at resonance. What is special about this diagram?
Q12. How does a phasor diagram help in calculating the impedance of a series AC circuit?
Long Answer Questions
Q13. Explain the concept of phasors with the help of a diagram. Show how a sinusoidal quantity V = Vโ sin(ฯt) can be represented as a rotating phasor.
Q14. Draw the complete phasor diagram for a series LCR circuit when X_L > X_C. Show all voltage phasors and derive the expression for the resultant voltage using the phasor addition method.
Q15. Explain the impedance triangle for a series LCR circuit. How is it related to the voltage phasor diagram? Show how the power factor can be determined from the impedance triangle.
Numerical & Application-Based Problems
Q16. In a series LR circuit, R = 30 ฮฉ and X_L = 40 ฮฉ. The applied voltage is V = 100 sin(100ฯt) volts.
(a) Draw the phasor diagram for this circuit.
(b) Calculate the impedance of the circuit.
(c) Determine the phase angle by which voltage leads the current.
(d) Write the expression for the instantaneous current.
Q17. A series LCR circuit has R = 10 ฮฉ, L = 0.1 H, and C = 50 ฮผF. It is connected to a 100 V, 50 Hz AC source.
(a) Calculate X_L and X_C.
(b) Draw the phasor diagram showing all voltage phasors.
(c) Calculate the impedance and the phase angle.
(d) Determine whether the circuit is predominantly inductive or capacitive.
Q18. In your school's physics lab, a student is asked to analyze an unknown series AC circuit using phasor diagrams. The student measures the following voltages across the components when a current of 2 A flows: V_R = 40 V, V_L = 60 V, V_C = 30 V. The applied voltage is measured as 50 V.
(a) Verify whether these readings are consistent with phasor addition.
(b) Draw the phasor diagram to scale (use a scale of 1 cm = 10 V).
(c) From your diagram, determine the phase angle between the applied voltage and the current.
(d) Calculate the resistance, inductive reactance, and capacitive reactance of the circuit.
(e) A classmate argues that since V_L + V_C = 90 V and V_R = 40 V, the applied voltage should be โ(90ยฒ + 40ยฒ). Point out the error in this reasoning and explain the correct method.