Maybe you can assist me with one small thing. wherever I see a plot of current v. frequency for capacitors and coils, one is always pretty mcuh a straight line whereas the ohter looks like exponential. Give that the formlulas are XC=1/wC and XL=wL and there's no square in either, where does the exponential character of one of the curve come from?
Draw the line y=1/x and all will be revealed.
Plot 1/x vs x -it is an inverse function, not an exponential. Also plotexp^-x exp^-x will be 1 at x=0 while 1/x will be infinite at x=0. The curves are quite different.
Plot their impedances on log linear paper (logarithmic frequency or period) and their inverse relationship is obvious. It is the linear frequency scale that is distorting the ratiometric relationship.
Okay, thnx, guys. well that explains the mathematics. Now on to the physics. I'd always tought of caps and coils as like mirror-images of each other in the way they act WRT signals applied. In every ohter respect AFAIA, this is true. Why then, is the response of one linear and the other hyperbolic?? I'm not asking for a re-iteration of the math here; what's the pysical processes going on that account for it?
They ARE both linear.
well I wonder why they don't mention that rather important little fact in the text books!!! :-(
It all depends on the textbook.
Tom
In all the ones I've seeen, they don't show any graduations on the plot panes at all. Then they say they don't because "precise values aren't important its the relationship between current and Xc and Xl that we're looking at here."
Sorry for a mistake. That should have read "log log paper". In this form, the slope of the line is proportional ot the power. 1st power functions slope up to the right with a slope of one. Negative first power functions (1/x) slope up to the left with a negative one slope.
---------- At DC a capacitance looks like an open circuit but at high frequency its impedance is very small so that the impedance drops from infinity to 0 as the frequency goes from 0 to infinity. If you plotted 1/Xc against frequency you would get a straight line.
At DC an inductor has an impedance of 0 and the impedance rises linearly with frequency. Try plotting 1/Xl vs frequency.
As for the physics -calculus rears its ugl head: Inductor: v=Ldi/dt which for steady state sinusoidal AC leads to V/I =2*pi*f*L in magnitude. Capacitor: v =charge /C = 1/C (integral of current) which leads, for steady state sinusoidal AC to V/I =1/(2*pi*f*C)
Have something to add? Share your thoughts — no account required.
Ask the community — no account required