An AC generator 10 V ( rms ) at ( Rms ) at 200 rad //s is connected in series with a 50 `Omega ` Resistor , a `400 mH` inductor and a `200 muF ` capacitor . The rms voltage across the inductor is

Options

A. `2.5V`
B. `3.4 V`
C. `6.7 V `
D. `10.8 V`

Answer

D

Explanation

Given , ` E=10 V `
` omega = 200 rad//s`
` R= 50 Omega `
`L= 400 mH `
` C= 200 mu F `
we know that ,
` Z = sqrt(R^2 +(X_L-X_C)^2)`
` = sqrt((50)^2+(80-25 )^2)= sqrt((50)^2-(55)^2)`
` = sqrt(2500+3025)`
` Z= sqrt(5525) = 74.3 Omega `
` I = (E) /(Z ) =( 10) /( 74.3)=0.13459 A `
` E_(L)= IX _(L) = 0.13459 xx80`
`= 10.76 V or 10.8 V `