Please Help with a (supposedly) simple RL Circuit Problem

[travisk]

Hey guys, before I begin I just want to say "Hello, World!" since this is my first post on the forum and just want everyone to know that this forum is a lifesaver for me!

I'm in an Electronics Class in school; it's my first time dealing with electronic circuits/etc. and my professors/TAs are extremely unhelpful. This is the problem I have been stuck on for the past 3 days and I have nowhere else to turn:

A 100mH inductor and a 1k resistor are connected in series across a sine wave generator with output of 10V at 1.6kHz. What is the voltage across the inductor? What is the voltage across the resistor?

Now I figured for the first part I would have to use the equation V = L dI/dt to figure out the voltage drop across the inductor and then subtract it from the 10V, however I HAVE NO IDEA HOW TO DEDUCE dI/dt!!! And also, wouldn't V just equal 10V if that's what the generator is outputting?

Then for the resistor, I would have to calculate the impedance, but again, how do I calculate the voltage for it without a current value??

Please help I as well as everyone in my class am super stuck and could really use the help. Thanks so much!

Best,
~Travis

 

[(*steve*)]

Ok, here's a hint. The impedance of a resistor is simply it's resistance.

 

[Laplace]

The same problem you describe is solved in section "9-4 First-Order System Excited by a Sinusoidal Wave" in the book Linear Circuits by Ronald E. Scott, pp 298-301, published by Addison-Wesley, 1960.

However, it is not clear whether your answer should be just the steady state solution. If so, then you have a frequency-domain network which you are trying to solve using time-domain methods. But Scott gives the following caveat in his book:

"Before studying frequency-domain methods, the student should review the solution of steady-state sinusoidal problems by the methods of classical differential equations. To appreciate the simplicity of the frequency-domain methods, the student must obtain the sinusoidal solution to at least one differential equation. The classical solution is straightforward, but is laborious and it involves the use of many trigonometric formulas. The frequency-domain method reduces the differential equation to an algebraic equation, and the trigonometry to complex algebra. It is a great deal easier!"

Perhaps your professors/TAs are extremely unhelpful because they already know that nobody in the real world ever tries to solve these kind of frequency-domain problems using time-domain methods.

 

[lexroxas]

What is the voltage across the inductor?
What is the voltage across the resistor?

1. You need to find the total current to find the voltages you require.
2. To find the total current, first you need to find the impedance of the series circuit.
3. To find the impedance of the series RL circuit, you find the algebraic sum of R and XL.

And now that you know the total current, use ohms law to solve the voltages you require. Study well.

 

[duke37]

lexrosas point 3
The impedance of a series RL circiut is not the arithmetic sum but Z=SQRT(R*R+X*X)

 

[lexroxas]

Ah yes! Thanks for the correction.

The impedance (Z) is the square root of the sum of the squares of R and XL.