# LC circuits

1. Nov 25, 2006

### rich t

It's been a while since i did physics at Uni and i'm a bit rusty with it all but i've recently been trying to get my head around LC circuits

i've looked at the wikipedia website and seen the solved differential for LC circuits but i'm a bit confused with the following assumptions...

current through inductor = -current through capacitor
voltage across capacitor = voltage across inductor

firstly, is there a current through the capacitor?! i can understand the idea of a current through the inductor but they aren't any electrons moving between the two plates are there, so how can there be a current?

secondly, if the voltage across capacitor = voltage across inductor how can there be any current flow? (i'm imagining two cells in a series circuit facing the opposite way) i have a feeling i've somehow misunderstood voltage here

i've been trying to get an intuitive idea of how these circuits work and i'm kind of thinking along these lines....

there is an intial build up of electrons on one plate of the capacitor (causing a voltage) there causes these electrons to move towards the other plate (a current flows). this current is limited because of the inductor, it cannot increase unchecked because of lenz's law, and so there is an opposing voltage due to the inductor (though i can't see how this could be the same size as the voltage across the capacitor?!)

but unlike a capacitor the current (and rate of change of voltage) increases, why?

i'm thinking if the rate of current increase were constant then the induced emf/voltage would be constant and since the voltage across the capacitor would decrease this would result in a drop in the rate of increase of current and so the inducred emf/voltage would decrease but since the current is still flowing the voltage across the capacitor would drop and so the rate of current increase would drop again....

if anyone could shed any light on this (particularly the point about the equal and opposite voltages) i'd be grateful

2. Nov 25, 2006

### tim_lou

well, the current through a capacitor is not really current, it is simply the rate of change of the charge on the capacitor, think of it as currents getting blocked by the plates in capacitor causing an accumulation of charges. Well, if you are interested in Maxwell's equation, there is a sort of fictitious current created by the capacitor, called displacement current. The change in the electric field in the capacitor is directly related to the "imaginary" current density.

3. Nov 26, 2006

### cesiumfrog

Draw the LC circuit. The amount of current through the inductor must be the same as is coming out of the capacitor because, well, where else can the electrons go?

The fact that there's a wire connecting the bottom of one to the bottom of the other should be a good hint that the bottom of both have the same potential (else, it would equalise almost instantly), likewise the top.