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…

Question

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

Aicharya · 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 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 ^

The instantaneous voltages at three terminals marked X ,   Y and Z are given by V X = V 0 sin ⁡…

Solution

The instantaneous voltages at three terminals marked X , &#160; Y and Z are given by V X = V 0 sin &#8289;…

Solution

The instantaneous voltages at three terminals marked X , Y and Z are given by V X = V 0 sin ⁡…