A series RCL circuit contains only a capacitor(C=8.80F), an inductor (L=4.30*10m

Question

A series RCL circuit contains only a capacitor(C=8.80F), an inductor (L=4.30*10mH) and a generator (peakvoltage=64.0, frequency=1.00*10^3 Hz). When t=0, the instantaneousvalue of the voltage is zero, and it rises to a maxium one-quarterof a period later.(a) find the instantaneous value of the voltageacross the capacitor/inductor combination whent=1.50*10^(-4)seconds ?(b)What is the instantaneous value of thecurrent when t=1.50*10^(-4) seconds? (Hint: the instantaneousvalues of voltage and current are, respectively, the verticalcomponents of the voltage and current phasors.) The answers in the back of my text book are (a)51.8V (b)-4.21A I keep trying to work it out but I can not get thatanswer This is what I have: Somebody please help me T=period=1/f, and f=1/t, the new t=1.50*10^(-4) seconds, sothe new f=6.67*10^3Hz, this is plugged into the equations for Xland Xc as follows Xl=2fL=180 Xc=1/(2fC)=2.71 to get Z, impedance, Z=(R^2+(Xl-Xc)^2)^(1/2)=177.3 To get Vrms=V/(2)^(1/2)=64/1.41=45.25 to get Irms=Vrms/Z=0.225 Then get Vc and Vl , which I am not sure but think they shouldadd up to be Vinstaneous??????? Vl=Irms*Xl=45.9 Vc=Irms*Xc=0.691 These two together Vl+Vc=46.59, which is not equal to51.8 Then Vi, Vinstaneous, Ii=Vi/Z, so Ii,instaneous=.263A   , which is not equalto -4.21A Someone please help me find where I am messing up, or guide meto help me achieve the right answer, I will rate well. A series RCL circuit contains only a capacitor(C=8.80F), an inductor (L=4.30*10mH) and a generator (peakvoltage=64.0, frequency=1.00*10^3 Hz). When t=0, the instantaneousvalue of the voltage is zero, and it rises to a maxium one-quarterof a period later.(a) find the instantaneous value of the voltageacross the capacitor/inductor combination whent=1.50*10^(-4)seconds ?(b)What is the instantaneous value of thecurrent when t=1.50*10^(-4) seconds? (Hint: the instantaneousvalues of voltage and current are, respectively, the verticalcomponents of the voltage and current phasors.) The answers in the back of my text book are (a)51.8V (b)-4.21A I keep trying to work it out but I can not get thatanswer This is what I have: Somebody please help me T=period=1/f, and f=1/t, the new t=1.50*10^(-4) seconds, sothe new f=6.67*10^3Hz, this is plugged into the equations for Xland Xc as follows Xl=2fL=180 Xc=1/(2fC)=2.71 to get Z, impedance, Z=(R^2+(Xl-Xc)^2)^(1/2)=177.3 To get Vrms=V/(2)^(1/2)=64/1.41=45.25 to get Irms=Vrms/Z=0.225 Then get Vc and Vl , which I am not sure but think they shouldadd up to be Vinstaneous??????? Vl=Irms*Xl=45.9 Vc=Irms*Xc=0.691 These two together Vl+Vc=46.59, which is not equal to51.8 Then Vi, Vinstaneous, Ii=Vi/Z, so Ii,instaneous=.263A   , which is not equalto -4.21A Someone please help me find where I am messing up, or guide meto help me achieve the right answer, I will rate well.

Explanation / Answer

given c = 8.80*10-6F L = 4.30*10-3H peak voltage = 64.ov frequency = f = 1.00*103 Hz the instaneous value of the currnt when time t =1.5*10-4s instaneous voltage = v(t) = V0sin2ft    plug in values = --------= -----v then XL = 2fL =2*3.14*4.30*10-3H *1.00*103 Hz =27    Xc = 1/2fc =1/2*3.14*8.80*10-6F *1.00*103 Hz = 18 since XL is greater tham Xc thecurrent lags the voltage by /2 radians thus the instaneouscurrent in the circuit is I(t) = I0 sin(2ft- /2) where I0 = V0/Z Z = R2 (XL -Xc)2 = 02 + (27-18)2 = 9 the instaneous current    I = V0/Z sin(2ft -/2) plug in values and do caliculations I =--------A

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