In the phasor diagram of an ac circuit, the length of the voltage phasor represents
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → the peak value of the voltage
An ac voltage is drawn as a phasor, a vector that rotates about the origin with angular speed \( \omega \). As it rotates, its vertical component changes. Its length stays the same.
Option (1) the rms value of the voltage — Incorrect. The rms value is \( v_m/\sqrt{2} \), which is less than the phasor length. Ac meters show this value.
Option (2) the instantaneous value of the voltage — Incorrect. The value at an instant is the projection of the phasor on the vertical axis, \( v_m\sin\omega t \). It changes as the phasor rotates.
Option (3) the peak value of the voltage — Correct. The length of the phasor is the amplitude \( v_m \), the largest value the voltage reaches in a cycle.
Option (4) the average value of the voltage over a cycle — Incorrect. A sine voltage is positive for half a cycle and negative for the other half. So its average over a cycle is zero, but the phasor has a fixed non-zero length.
NCERT (2026-27):
Representation of AC Current and Voltage by Rotating Vectors — Phasors – “… The magnitudes of phasors V and I represent the amplitudes or the peak values vm and im of these oscillating quantities. …”