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

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The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by
$V_{X} = V_{0} \sin ω t$
$V_{Y} = V_{0} \sin (ω t + \frac{2 π}{3})$ and
$V_{Z} = V_{0} \sin (ω t + \frac{4 π}{3}) .$
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

TestHub · Accepted Answer

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 peak = 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 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

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