The instantaneous voltages at three terminals marked X,Y and Z are given $$byVX=V0sin$$ωt, $$VY=V0sin$$ω$$t+2$$$$π$$$$3and$$ $$VZ=V0sin$$ω$$t+4$$$$π$$$$3An$$ 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

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The instantaneous voltages at three terminals marked X,Y and Z are given $$byVX=V0sin$$ωt, $$VY=V0sin$$ω$$t+2$$$$π$$$$3and$$ $$VZ=V0sin$$ω$$t+4$$$$π$$$$3An$$ 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

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The potential difference between X and Y points is $$VXY=VY$$−Vx⇒$$VXY=V0sin$$⁡ω$$t+2$$$$π$$$$3$$−$$V0sin$$⁡ωt Now, ϕ$$=2$$$$π$$$$3$$−$$0=2$$$$π$$$$3$$⇒$$VXY0=V02+V02$$−$$2V0V0cos$$⁡$$2$$$$π$$$$3=3V0$$ So, VXYrms $$=VXY02=3V02$$   Similarly, The potential difference between Z and Y points is $$VYZ=VZ$$−VY⇒$$VYZ=V0sin$$⁡ω$$t+4$$$$π$$$$3$$−$$V0sin$$⁡ω$$t+2$$$$π$$$$3$$ϕ$$=4$$$$π$$$$3$$−$$2$$$$π$$$$3=2$$$$π$$$$3$$⇒$$VYZ0=V02+V02$$−$$2V0V0cos$$⁡$$2$$$$π$$$$3=3V0$$ So, $$VYZrms=VYZ02=3V02$$ Similarly, The potential difference between Z and X points is $$VxZ=VZ$$−Vx⇒$$Vxz=V0sin$$⁡ω$$t+4$$$$π$$$$3$$−$$V0sin$$⁡$$($$ω$$t)$$ϕ$$=4$$$$π$$$$3$$−$$0=4$$$$π$$$$3$$⇒$$VxZ0=V02+V02$$−$$2V0V0cos$$⁡$$4$$$$π$$$$3=3V0$$ So ,$$VXZrms=Vxz02=3V02$$

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