*Hello all, I'm having some difficulty doing this problem. I feel like I'm nearly there so if anyone has a minute to help me out with the last few steps I'd really appreciate it.*

I know the formatting's not great - if requested I will have another go at formatting it a bit better..

I know the formatting's not great - if requested I will have another go at formatting it a bit better..

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Question:

**In a series RLC circuit the value of the inductance is 0.02H**

Find the values of the resistance and capacitance where the voltage and current are given by:

v(t) = 353.5 cos(3000t -10) V

i(t) = 12.5 cos(3000t -55) A

Find the values of the resistance and capacitance where the voltage and current are given by:

v(t) = 353.5 cos(3000t -10) V

i(t) = 12.5 cos(3000t -55) A

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Cos(x) = Sin(x + 90)

=> v(t) = 353.5 sin(3000t, -10 + 90)

= 353.5 sin(3000t, +80)

& i(t) = 12.5 sin(3000t, -55 + 90)

= 12.5 sin(3000t, +35)

=>

ω = 3000

=> Xl = 3000 * .02 = 60 Ω

=> Zl = 60 ∠ 90

Vpeak = 353.5

=> V = 353.5 * .707 = 249.9 ∠ 80

= 249.9 * cos(80) + j 249.9 * sin(80)

= 43.4 + j246.1

Ipeak = 12.5

=> I = 12.5 * .707 = 8.8 ∠ 35

= 12.5 * cos(35) + j 12.5 * sin(35)

= 7.2 + j 5.0

Ir = Il = Ic = Itotal = (7.2 + j 5.0) OR (8.8 ∠ 35)

Ztotal = Etotal / Itotal

= (249.9 ∠ 80) / (8.8 ∠ 35)

= (249.9/8.8) ∠ (80 - 35)

= 28.4 ∠ 45

= 28.4 * cos(45) + j 28.4 * sin(45)

= 20.1 + j 20.1

El = Il * Zl

= (8.8 ∠ 35) * (60 ∠ 90)

= (8.8 * 60) ∠ (35 + 90)

= 528 ∠ 125

= -302 + j 432.5

**So I now have values for El, Etotal, Ir, Il, Ic, Itotal, Zl, Ztotal - basically everything except Er, Ec, Zr and Zc. I'm just not sure how to go about the last portion of splitting the impedance between the inductor, capacitor and resistor.**

*Also - would anyone like to hazard a guess as to what percentage of the marks getting this far would get me in an exam situation?*

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