Consider the following statements about phasors in ac circuits:
(A) The vertical component of a phasor gives the value of the quantity at that instant.
(B) A phasor rotates anticlockwise about the origin with angular speed \(\omega\).
(C) For a resistor, the voltage and current phasors are perpendicular to each other.
(D) For a capacitor, the current phasor is \(\pi/2\) behind the voltage phasor.
Which of the above statements are incorrect?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (C) and (D) only
In a phasor diagram, each ac voltage or current is drawn as a vector that rotates about the origin. The angle between two phasors shows the phase difference between the two quantities.
(A) The vertical component of a phasor gives the value of the quantity at that instant. — Correct statement. The vertical component of V is \( v_m\sin\omega t \), which is the voltage at time \( t \).
(B) A phasor rotates anticlockwise about the origin with angular speed \( \omega \). — Correct statement. In a time \( t \) the phasor turns through an angle \( \omega t \). Its vertical component then traces the sine graph of the quantity.
(C) For a resistor, the voltage and current phasors are perpendicular to each other. — Incorrect statement. For a resistor, V and I point in the same direction at all times, because the voltage and the current are in phase.
(D) For a capacitor, the current phasor is \( \pi/2 \) behind the voltage phasor. — Incorrect statement. In a capacitor the current phasor is \( \pi/2 \) ahead of the voltage phasor. It is \( \pi/2 \) behind in an inductor.
NCERT (2026-27):
Representation of AC Current and Voltage by Rotating Vectors — Phasors – “… The projection of voltage and current phasors on vertical axis, i.e., vm sinωt and im sinωt, respectively represent the value of voltage and current at that instant. …”
Summary – “… A phasor is a vector which rotates about the origin with angular speed ω. …”
Representation of AC Current and Voltage by Rotating Vectors — Phasors – “… phasors V and I for the case of a resistor are in the same direction. This is so for all times. …”
AC Voltage Applied to a Capacitor – “… Here the current phasor I is π/2 ahead of the voltage phasor V as they rotate counterclockwise. …”