Determining steady state current from phasor current?

In summary, the phasor current for the circuit is 7.87∠45°A and the impedance is 12.7∠-45°Ω. The steady-state current can be represented as i(t) = 7.87cos(100t + 45)A. It is important to specify units and to keep track of decimal places to prevent rounding errors.
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Homework Statement

[Broken]
a) Determine the phasor current and impedance of the circuit

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

Homework Equations



impedance conversion:

ZL = ωLj

ZC = -1j/ωC

ZR = 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

Zr = 9ΩZC = -1j/(100*(1x10-3))

ZC = -10ΩjZL = 100 * (10 x 10-3)

ZL = 1Ωj

Ztotal = 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) ?
 
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  • #2
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.
 

1. What is a steady state current?

A steady state current refers to the constant flow of electric current in a circuit after all transient effects have died out. It is the current that remains once the circuit has reached a state of equilibrium.

2. How is steady state current different from phasor current?

Steady state current represents the actual flow of current in a circuit, while phasor current is a simplified representation of the time-varying current using complex numbers. Phasor current is used in AC circuits to simplify calculations and analysis.

3. What factors affect the determination of steady state current from phasor current?

The determination of steady state current from phasor current is affected by the circuit topology, the values of the electrical components, and the frequency of the AC source. These factors determine the magnitude and phase of the steady state current.

4. How can phasor current be converted to steady state current?

To convert phasor current to steady state current, the complex phasor must be multiplied by the complex impedance of the circuit. This will result in a steady state current with the same magnitude and phase as the phasor current.

5. Why is it important to determine steady state current from phasor current?

Determining steady state current from phasor current is important in the analysis and design of AC circuits. It allows for the calculation of power, voltage, and current at any point in the circuit, and enables engineers to optimize circuit performance and ensure safe operation.

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