Electromagnetic Induction And Alternating Current Ques 80
80. The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by $V_{X}=V_{0} \sin \omega t$,
$V_{Y}=V_{0} \sin \Big(\omega t+\frac{2 \pi}{3})$ and $V_{Z}=V_{0} \sin \Big(\omega t+\frac{4 \pi}{3})$.
An ideal voltmeter is configured to read the peak 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
(2017 Adv.)
(a) $(V _ {Y Z}) _ {\mathrm{rms}}=V _ {0} \sqrt{\frac{1}{2}}$
(b) $(V _ {X Y}) _ {\mathrm{rms}}=V _ {0} \sqrt{\frac{3}{2}}$
(c) independent of the choice of the two terminals
(d) $(V _ {X Y}) _ {\mathrm{rms}}=\frac{V _ {0}}{\sqrt{2}}$
Show Answer
Answer:
Correct Answer: 80.(b, c)
Solution:
Formula:
$V_{X Y}=V_{0} \sin \left(\omega t+\frac{2 \pi}{3}\right)$
$$ V_{0} \sin \omega t+\frac{2 \pi}{3}+V_{0} \sin (\omega t+\frac{2 \pi}{3}) $$
$$ \Rightarrow \quad \varphi=\pi-\frac{2 \pi}{3}=\frac{\pi}{3} $$
$\Rightarrow \quad V_{0}{ }^{\prime}=2 V_{0} \cos \frac{\pi}{6}=\sqrt{3} V_{0}$
$\Rightarrow \quad V_{X Y}=\sqrt{3} V_{0} \sin (\omega t+\varphi)$
$\Rightarrow \quad (V _ {X Y}) _ {\mathrm{rms}}= (V _ {Y Z}) _ {\mathrm{rms}}=\sqrt{\frac{2}{3}} V _ {0}$
BETA
