Do not understand Solution to this problem (AC Circuit Analysis)

[Xyius]

Homework Statement

See The attached Images.

2. The attempt at a solution

The problem I am having with this is the following.

I do not know where he is getting these equations from. We haven't done anything like this in class. Although he keeps mentioning skills we learned in previous courses, which I took at another institution so it wasn't all exactly the same.

I see what looks like normalization constants from Fourier analysis? (2/pi) And square roots of 2 (usually indicates RMS). But I do not know the logic behind the equation. Also, why is he using "X" to indicate resistance? Is it a reactance? I also don't know where he gets the expression for the phase "u."

Sorry I know this might seem like a silly question but if anyone can help me out I would really appreciate it!

 

[rude man]

Homework Statement

See The attached Images.

2. The attempt at a solution

The problem I am having with this is the following.

I do not know where he is getting these equations from. We haven't done anything like this in class. Although he keeps mentioning skills we learned in previous courses, which I took at another institution so it wasn't all exactly the same.

I see what looks like normalization constants from Fourier analysis? (2/pi) And square roots of 2 (usually indicates RMS). But I do not know the logic behind the equation. Also, why is he using "X" to indicate resistance? Is it a reactance? I also don't know where he gets the expression for the phase "u."

Sorry I know this might seem like a silly question but if anyone can help me out I would really appreciate it!

X is the universal symbol of reactance: Z = R + jX. X = wL for inductor and -1/wC for capacitor. X is in Ohms.

I can't make out the text in the 1st (your work) slide.

 

[NascentOxygen]

It looks like this might be using design approximations used for inductive smoothing at the output of a bridge rectifier. The flattened current waveform suggests you can assume very effective smoothing. That constant current indicates why you can represent the load as a fixed voltage source: a steady current into a fixed load is just like a fixed voltage in opposition.

The topic may be discussed in your textbook, otherwise search for worked examples online.

 

[NascentOxygen]

The handwriting is very clear and easy to read on my tablet, anyway.

 

[NascentOxygen]

I do not know where he is getting these equations from. We haven't done anything like this in class. Although he keeps mentioning skills we learned in previous courses, which I took at another institution so it wasn't all exactly the same.

Have you asked others in the class about these formulae? In any subject, your best resource is always other students in your class.

 

[rude man]

The handwriting is very clear and easy to read on my tablet, anyway.

So's mine. I was referring to the printed text.