A resistor R=500Ω, an ideal inductor L=0.9 H and a capacitor C=2.5μF are connected with two alternating source e1=100 sin(1000t) and e2=1003cos(1000t). V1,V2,V3,V4 and V5are five ideal voltmeters and connected in the circuit as shown in the figure. Choose the correct option(s).

Phase difference between voltage of V 3 and V 5 is π 2 + tan − 1 ( 9 5 ) , Difference between reading of V 2 and V 1 is 80 volt. , Reading of V 4 is 180 volt

A resistor R=500Ω, an ideal inductor L=0.9 H and a capacitor C=2.5μF are connected with two alternating source e1=100 sin(1000t) and e2=1003cos(1000t). V1,V2,V3,V4 and V5are five ideal voltmeters and connected in the circuit as shown in the figure. Choose the correct option(s).

e = e 1 + e 2 = 200 sin ( ωt + π 2 ) e 0 = 200 volt V 5 = 200 2 = 100 2 z = ( 500 ) 2 + ( 500 ) 2 = 500 2 i rms = 100 2 500 2 = 1 5 V 1 = 500 × 1 5 = 100 volt V 2 = 900 × 1 5 = 180 volt V 3 = 400 × 1 5 = 80 volt V 4 = V 2 − V 3 = 100 volt ⇒ ϕ = π 2 + tan − 1 ( 9 5 ) <img src="data:image/png;base64,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">

Phase difference between voltage of V 3 and V 5 is π 2 + tan − 1 ( 9 5 )

Ratio of reading of V 4 and V 5 is 1 2

Difference between reading of V 2 and V 1 is 80 volt.

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A resistor $R = 500 Ω$ , an ideal inductor L=0.9 H and a capacitor $C = 2.5 μF$ are connected with two alternating source $e_{1} = 100 \sin (1000 t)$ and $e_{2} = 100 \sqrt{3} \cos (1000 t)$ . $V_{1}, V_{2}, V_{3}, V_{4} and V_{5}$ are five ideal voltmeters and connected in the circuit as shown in the figure. Choose the correct option(s).

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

Phase difference between voltage of $V_{3} and V_{5}$ is $\frac{π}{2} + \tan^{- 1} (\frac{9}{5})$

Ratio of reading of $V_{4} and V_{5} is \frac{1}{\sqrt{2}}$

Difference between reading of V₂ and V₁is 80 volt.

Reading of V₄ is 180 volt

answer is A, C, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$e = e_{1} + e_{2} = 200 \sin (ωt + \frac{π}{2}) e_{0} = 200 volt$
$V_{5} = \frac{200}{\sqrt{2}} = 100 \sqrt{2} z = \sqrt{{(500)}^{2} + {(500)}^{2}} = 500 \sqrt{2}$