If Vin=2cos(1000*pi*t) and C=2.2 uF (micro) Find the phasor relation Vout=ZcI? (

Question

If Vin=2cos(1000*pi*t) and C=2.2 uF (micro)

Find the phasor relation Vout=ZcI? (little c means capacitor impedance)

i found Zc=-144.7 (-90) then combined it with Zr=560 (0) to get Z=578.4 (-14.49)

then i found I=Vin/Z I=(3.46*10^-3) (14.49) then i found Vout=0.5 (-75.5) is this correct? could you show working if it isn't thanks.

sorry about it being a bit hard to read but i dont know what to use for phase angle when typing other than brackets, thanks in advance for any assistance and i will rate answers.

Explanation / Answer

Zc=1/jwC = 1/(j*1000**2.2*10^-6)

Zc=144.7 (-90)------------------there will be no negative sine as the angle has negative sign

Zr=560 (0)--------------correct

I = Vin/Z = 2(0) / [ 144.7 (-90) + 560(0) ]

    = 3.45*10^-3*(14.48) A

Vout = Zc * I

       = 144.7 (-90) *3.45*10^-3*(14.48)

      = 0.5 ( -75.52)

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