(1/7) A series RLC circuit with L = 22.5 mH, C = 4 µF, and R = 15 is driven by a
ID: 1505804 • Letter: #
Question
(1/7) A series RLC circuit with L = 22.5 mH, C = 4 µF, and R = 15 is driven by a generator with a maximum emf of 100 V and a variable angular frequency . Find the resonant frequency 0. Answer in units of rad/s.
(2/7) Find the Irms at resonance. Answer in units of A.
(3/7) Find XC when = 10000 rad/s. Answer in units of .
(4/7) Find XL when = 10000 rad/s. Answer in units of .
(5/7) Find Z when = 10000 rad/s. Answer in units of .
(6/7) Find Irms when = 10000 rad/s. Answer in units of A.
(7/7) Find the phase angle when = 10000 rad/s. Answer in units of .
Explanation / Answer
1) for resonant frequency, w0
Xc = XL
1/w0C = w0 L
w0 = 1 / sqrt(LC)
w0 = 1 / sqrt(22.5 x 10^-3 x 4 x 10^-6)
w0 = 3333.33 rad/s ...........Ans
2) at w0 ,
Z = R = 15 ohm
I = Vrms / Z and Vrms = Vmax /sqrt(2) = 100 / sqrt(2) = 70.71 V
I = 70.71 / 15 = 4.71 A .........Ans
3) Xc = 1 / wC = 1/ (10000 x 4 x 10^-6 ) = 25 ohm
4) XL = wL = 10000 x 22.5 x 10^-3 =225 ohm
5) Z = sqrt[ R^2 + (XL - Xc)^2 ]
= sqrt[ 15^2 + (225- 25)^2 ] = 200.56 ohm
6) Irsm = Vrms / Z = 70.71 / 200.56 = 0.35 A
7) phase angle, @ = tan^-1[ (XL - Xc) / R ]
= tan^-1 [ (225 - 25) / 15 ]
= tan^-1 [ 200/15 ] = 85.71 deg
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