Problem with inductors and Capacitors in Series (AC Theroy)

[iceman_ch]

Homework Statement

Find the steady state expresion for i(t) in the circuit if Vs=750 Cos(5000t) mV

All componets are in series

Resitor = 400 Ohms
Inductor = 40mH
Cap = .4 $$\mu$$F

Homework Equations

Xc= 1/(j*w*C)
Xl = j*w*L
Xr = R

The Attempt at a Solution

Ok I know how to do most of the problem but, when I look at the teachers solution it throws me off. What I would do is first find the impedences of all of the componets and then add them toghether to find the total. Then divide the voltage by the impedence and viola all done. My dilema is what frequency to use. I started out by using 5000 but, when I look at the teachers solution he used 5. I'm assuming this is because of the mV but, I thought that the frequency is independent from the voltage. It shouldn't matter what units of voltage are there since it's just a scalar. Anyways any help would be apprecieted.

Thanks

 

[iceman_ch]

Nevermind I figured out what he was doing. He was simply droping zeros and moving the decimal points. grrrr stupid mistake.

 

[Mene]

Dear student,

Thank you for sharing your thoughts and concerns about this problem. It is always a good idea to check your work against a teacher's solution to ensure accuracy and understanding.

In this case, the frequency does not depend on the units of voltage, but rather on the units of time. The frequency in this circuit is given as 5000t, where t is time in seconds. This means that the frequency is 5000 Hz, or 5 kHz. This is why your teacher used 5 instead of 5000 in the calculation.

Additionally, your approach of finding the impedances of each component and adding them together is correct. This will give you the total impedance of the circuit, which can then be used to find the current using Ohm's Law.

I hope this helps clarify any confusion and good luck with your studies! Remember, when in doubt, always check your work and ask for help if needed. Keep up the good work as a scientist!