Note added: homework 7 is canceled. I will post some potentially important and hopefully interesting practice problems instead.
HW #7 includes questions about circuits with L, C and R type elements. Please feel free to comment if some of these problems see impossible to do with what we have covered and emphasized in class. I will modify the HW later if that seems like a good idea.
In order for you to understand the nature oscillating LC circuits and LCR circuits, it is critically important for you to be quite familiar with sine and cosine functions, as well as exponential functions.
What does cos(wt) look like from wt=0 to pi/2 ?
What does sin(wt) look like from wt=0 to pi/2 ?
Why does it seem reasonable, looking at the graphs, that the derivative of cos(wt) is -wsin(wt)?
etc...
If you can achieve that familiarity, then you will be able to visualize, understand and discuss the behavior of circuits, which will be a major point of emphasis for he final.
Consider the function: sin(wt), where w has units of 1/seconds, also known as frequency and t is time. What is its value at t=0? Can you graph this function? What is its highest value? What is its lowest value? What is its period? These questions are best answered by looking at a graph and seeing and understanding what the function looks like -- how it goes up and down and repeats as a function of time.
The function, cos(wt), is equally important. Unlike the sine function it starts out at 1, at t=0, but just like the sine function, it oscillates up and down and repeats as a function of time. What does cos(wt) look like when it is multiplied by exp{-t/tau}...
Student question: "I'm having trouble determining which direction current goes. It keeps coming up in the hw but, the explanation don't make sense to me. In an LC circuit does it just go to the inductor first? I also can't tell in RL and RC circuits. Can you clear this up for me?"
ReplyDeletein our circuits the current is the same everywhere in the circuit. It depends only on time, not on "position". As far as direction, it can be either counter-clockwise or clockwise.
ReplyDeleteThus one cannot say that, "it goes into the inductor first...". At any given time, it is the same everywhere in the circuit*. (*for our uncomplicated, series circuits).