# Homework Help: Determining steady state current from phasor current?

1. Jun 15, 2013

### Color_of_Cyan

1. The problem statement, all variables and given/known data

[Broken]

a) Determine the phasor current and impedance of the circuit

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

2. Relevant equations

impedance conversion:

ZL = ωLj

ZC = -1j/ωC

ZR = R

Polar form conversion:

rectangular form = R + jX

Zmag = (j2 + r2)1/2

Zangle = arctan(j/r)

V = IR

I=V/R

3. The attempt at a solution

ω = 100

Zr = 9Ω

ZC = -1j/(100*(1x10-3))

ZC = -10Ωj

ZL = 100 * (10 x 10-3)

ZL = 1Ωj

Ztotal = 9Ω - 9Ωj

In 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°)A

Now, I am actually stuck how to get the steady state current but I think it's something in waveform like

i(t) = 7.87cos(100t + 45) ?

Last edited by a moderator: May 6, 2017
2. Jun 15, 2013

### Staff: Mentor

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.