Determining steady state current from phasor current?

[Color_of_Cyan]

Homework Statement

a) Determine the phasor current and impedance of the circuit

b) Determine the steady-state current i(t).

Homework Equations

impedance conversion:

Z_L = ωLj

Z_C = -1j/ωC

Z_R = RPolar form conversion:

rectangular form = R + jX

Zmag = (j² + r²)^1/2

Zangle = arctan(j/r)V = IR

I=V/R

The Attempt at a Solution

ω = 100

Z_r = 9ΩZ_C = -1j/(100*(1x10^-3))

Z_C = -10ΩjZ_L = 100 * (10 x 10^-3)

Z_L = 1Ωj

Z_total = 9Ω - 9ΩjIn polar form:

Zmag = (81 + 81)^1/2

Zmag = 12.7

Zangle = arctan(-9/9)

Zangle = -45°

So

Z = 12.7∠-45°

and

V = 100∠0°I = V/R

I = (100∠0°)/(12.7∠-45°)Phasor current I = (7.87∠45°)ANow, I am actually stuck how to get the steady state current but I think it's something in waveform likei(t) = 7.87cos(100t + 45) ?

 

[gneill]

Yes, that's fine. Be sure to specify the units on the answer.

Also remember to hang onto a few more decimal places in intermediate steps to prevent rounding error from creeping into your values as calculations progress.