The instantaneous voltages at three terminals marked X , Y and Z are given by V X = V 0 sin ⁡ ω t V Y = V 0 sin ⁡ ω t + 2 π 3 and V Z = V 0 sin ⁡ ω t + 4 π 3 . An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z . The reading(s) of the voltmeter will be

Step-by-step solution

Potential difference between X a n d Y = V X - V Y Potential difference between Y a n d Z = V Y - V Z Phasor of the voltages: From phasor diagram the peak value of V x - V y can be calculated from parallelogram law V x - V y p e a k = V X 2 + V Y 2 + 2 V X V Y cos 60 = V 0 2 + V 0 2 + 2 V 0 V 0 × 1 2 = 3 V 0 ∴ V X - V Y p e a k = 3 V 0 V x - V y r m s = V X Y r m s = 3 V 0 2 Similarly V y - V z r m s = V X Y r m s = 3 V 0 2