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

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 +(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 (A) Vrmsxy = V0√(3/2) (B) Vrmsxy = V0√(1/2) (C) Vrmsxy = V0 (D) independent of the choice of the two terminals

Tardigrade Admin · Accepted Answer

V XYO = V Y 2 O = V ZXO =√3 V 0 V XX ms = V YZ rms =√(3/2) V 0

$V_{x y}^{r m s} = V_{0} \frac{3}{2}$

$V_{x y}^{r m s} = V_{0} \frac{1}{2}$

$V_{x y}^{r m s} = V_{0}$

independent of the choice of the two terminals

$V_{X Y O} = V_{Y 2 O} = V_{ZXO} = 3 V_{0}$
$V_{XX}^{m s} = V_{Y Z}^{r m s} = \frac{3}{2} V_{0}$

Vxyrms​=V0​23​​

Vxyrms​=V0​21​​

Vxyrms​=V0​

independent of the choice of the two terminals

VXYO​=VY2O​=VZXO​=3​V0​ VXXms​=VYZrms​=23​​V0​

$V_{x y}^{r m s} = V_{0} \frac{3}{2}$

$V_{x y}^{r m s} = V_{0} \frac{1}{2}$

$V_{x y}^{r m s} = V_{0}$

$V_{X Y O} = V_{Y 2 O} = V_{ZXO} = 3 V_{0}$
$V_{XX}^{m s} = V_{Y Z}^{r m s} = \frac{3}{2} V_{0}$