• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Converting phasor back into time domain

1. Homework Statement
Find Amplitude of Steady-state voltage across capacitor

2. Homework Equations


3. The Attempt at a Solution
5a96193ba4.jpg

d57119ca1c.jpg


I'm at the very last step of changing it back into the time domain to obtain my ampltiude. I was planning on getting it into the form a + bj, then using trigonometry and other formulae to get it into polar form from which I can get it into the form of Bsin(wt + theta), with B giving me my amplitude.

Im stuck with 8+ 8/20 j^-1. Which isnt in the form a+bj. Any ideas how I can try and get it into that form?
 

NascentOxygen

Mentor
9,189
1,041
There is no specific frequency information contained in that complex number. The frequency of all voltages and currents will be that of the driving signal.

Your complex number yields an angle and an amplitude.

How to view ##\dfrac 1j##? Multiply both numerator and denominator by ##j## and see where that leads.

BTW, ##\frac 8 {1+j20}## is not equal to what you say. Instead, multiply numerator and denominator by the complex conjugate of the denominator so you can end up with a real denominator.
 
There is no specific frequency information contained in that complex number. The frequency of all voltages and currents will be that of the driving signal.

Your complex number yields an angle and an amplitude.

How to view ##\displaystyle {\dfrac 1j}##? Multiply both numerator and denominator by ##j## and see where that leads.
The frequency comes from the initial voltage sinusoid of 10rads/s. Phasors don't have frequencies.

If I multiply above and below by j. I get:

gif.latex?8%20+%20%5Cfrac%7B8%7D%7B20j%7D.gif
 

gneill

Mentor
20,486
2,610
Check your voltage division work. The numerator of the fraction should contain the impedance of the component that you want the voltage across and the denominator the sum of the two impedances.

Regarding your conversion to time domain, take your rectangular form and convert it to polar form (magnitude and angle). You then have the magnitude and phase angle for the time domain.
 
Check your voltage division work. The numerator of the fraction should contain the impedance of the component that you want the voltage across and the denominator the sum of the two impedances.

Regarding your conversion to time domain, take your rectangular form and convert it to polar form (magnitude and angle). You then have the magnitude and phase angle for the time domain.
Ah.. My Voltage division is wrong. I accidently used the formula for resistors in parallel. oops
 

NascentOxygen

Mentor
9,189
1,041
Your expression for V right back at the start is wrong. Pretend you have resistors and write the expression, then substitute the capacitor impedance for one of the resistances.
 

gneill

Mentor
20,486
2,610
By the way, the following is definitely not true:
upload_2016-11-13_11-27-17.png


You can't split a denominator like that, even for real values. Consider an example:

##\frac{8}{6 + 2} \ne \frac{8}{6} + \frac{8}{2}##
 
By the way, the following is definitely not true:
View attachment 108847

You can't split a denominator like that, even for real values. Consider an example:

##\frac{8}{6 + 2} \ne \frac{8}{6} + \frac{8}{2}##
Okay. why am i being so stupid today. Apologies for all these stupid mistakes. Let me redo the question.
 
Okay. So I got

gif.latex?V%20%3D%20%5Cfrac%7B4%7D%7Bj20%20+%201%7D.gif


Now. How do I transform that into the form a+bj.?
 

gneill

Mentor
20,486
2,610
Okay. So I got

gif.latex?V%20%3D%20%5Cfrac%7B4%7D%7Bj20%20+%201%7D.gif


Now. How do I transform that into the form a+bj.?
That's standard complex math: multiply the numerator and denominator by the complex conjugate of the denominator.
 

Want to reply to this thread?

"Converting phasor back into time domain" You must log in or register to reply here.

Related Threads for: Converting phasor back into time domain

  • Posted
Replies
7
Views
2K
Replies
5
Views
867
Replies
11
Views
3K
Replies
4
Views
6K
Replies
7
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top