# Understanding LC Circuits: Voltage & Current Explained

• rich t
In summary: So there's a potential difference between the two, created by the wire connecting them. And that difference in potential created an electric field.
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

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.

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.

## 1. What is an LC circuit and how does it work?

An LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected in series. When an electrical current flows through the circuit, the inductor stores energy in the form of a magnetic field, while the capacitor stores energy in the form of an electric field. As the energy oscillates back and forth between the inductor and the capacitor, the circuit produces a continuously changing voltage and current.

## 2. How does the voltage and current behave in an LC circuit?

In an LC circuit, the voltage and current are out of phase with each other. This means that when the voltage is at its maximum, the current is at its minimum, and vice versa. As the energy oscillates between the inductor and the capacitor, the voltage and current will continue to alternate between maximum and minimum values.

## 3. What is resonance in an LC circuit?

Resonance is a phenomenon that occurs in an LC circuit when the frequency of the alternating current matches the natural frequency of the circuit. At resonance, the inductive and capacitive reactances cancel each other out, resulting in a minimum impedance and maximum current flow. This causes the voltage across the circuit to reach its maximum value.

## 4. How does the voltage and current change over time in an LC circuit?

Initially, when the circuit is first turned on, the voltage across the inductor is at its maximum, and the current across the capacitor is at its minimum. As time passes, the energy stored in the magnetic field of the inductor decreases, causing the voltage to decrease and the current to increase. Eventually, the energy will be fully transferred to the capacitor, and the voltage will reach its minimum value, while the current reaches its maximum value. The energy will then continue to oscillate back and forth between the inductor and the capacitor, causing the voltage and current to alternate between maximum and minimum values.

## 5. What are some real-world applications of LC circuits?

LC circuits have many practical applications, including in radio and television broadcasting, where they are used to tune in to specific frequencies. They are also used in electronic filters, such as in audio equipment, to remove unwanted frequencies. LC circuits are also used in devices like pacemakers and defibrillators, where they provide a steady and controlled electrical current.

• Introductory Physics Homework Help
Replies
5
Views
372
• Classical Physics
Replies
15
Views
419
• Other Physics Topics
Replies
22
Views
4K
• Electromagnetism
Replies
6
Views
1K
• Electrical Engineering
Replies
21
Views
1K
• Electrical Engineering
Replies
13
Views
2K
• Other Physics Topics
Replies
8
Views
5K
• Introductory Physics Homework Help
Replies
8
Views
314
• Introductory Physics Homework Help
Replies
20
Views
565
• Other Physics Topics
Replies
3
Views
1K