The instantaneous voltages at three terminals marked X, Y and Z are given by [
`" "V_(x)=V_(0)sinomegat`,
`" "V_(Y)=V_(0)sin(omegat+(2pi)/3)` and
`" "V_(Z)=V_(0)sin(omegat+(4pi)/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

Options

A. `V_(XY)^(rms) = V_(0) sqrt((3)/(2))` .
B. `= V_(YZ)^(rms) = V_(0) sqrt((1)/(2))`.
C. independent of the choice of the two terminals.
D. `V_(XY)^(2)rms) = V_(0)`.

Answer

A, C

Explanation

(a,c ) : `V_(xy) = V_(x) -V_(y) = (V_(xy))_(0) sin ( omegat + Phi_(1))`
Phase difference between X and Y is `2 pi //3 `.
`(V_(xy))_(0)=sqrt(V_(0)^(2)+V_(0)^(2)-2V_(0)^(2)cos""(2pi)/(3) )=sqrt(3V_(0))`
`(V_(xy))_("rms")= ((V_(xy))_(0))/(sqrt(2))=sqrt((3)/(2))V_(0)`
Hence option (a) is correct.
`V_(yz)= V_(y)=V_(z) = (V_(yz))_(0)sin (omegat+Phi_(2))`
Phase difference between Y and Z is also `2pi//3` .
`(V_(yz))_(0)= sqrt(V_(0)^(2)+V_(0)^(2)-2V_(0)^(2)cos""(2pi)/(3) )=sqrt(3)V_(0)`
`(V_(yz))_("rms") = ((V_(yz))_(0))/(sqrt(2))=sqrt((3)/(2))V_(0)`
Hence option (b) is wrong .
In case of AC circuit polarity keeps changing , hence reading is not dependent on the choice of the terminals . Option ( c ) is corret .
Option (d) cannot be correct beause option ( a) is correct.