LC Resonant Circuit

[iamakda]

Hi,

I have a query on capacitor's charging and discharging behavior (pattern) in parallel LC resonant circuit.

Normally, we see that capacitor discharges exponentially which is proven mathematically. The exponent term in the mathematical equation shows that capacitor discharges exponentially.

However, when we talk about parallel LC resonance circuit, there the capacitor's charging and discharging is not exponential but sinusoidal. And we notice sinusoidal oscillations out of LC tank circuit.

Could anyone explain why it (capacitor discharging and charging) is sinusoidal and not exponential in LC tank circuit?

Thanks.

[Longbow]

Re: LC Resonant Circuit

Sir, you are confusing the time domain with the frequency domain. See: LaPlace, Fourier, Euler.

[keeney123]

Re: LC Resonant Circuit

Hi,

I have a query on capacitor's charging and discharging behavior (pattern) in parallel LC resonant circuit.

Normally, we see that capacitor discharges exponentially which is proven mathematically. The exponent term in the mathematical equation shows that capacitor discharges exponentially.

However, when we talk about parallel LC resonance circuit, there the capacitor's charging and discharging is not exponential but sinusoidal. And we notice sinusoidal oscillations out of LC tank circuit.

Could anyone explain why it (capacitor discharging and charging) is sinusoidal and not exponential in LC tank circuit?

Thanks.

We know it as "Eli" the "Ice" man. Where E = Voltage, I = Current, L = inductor, C = capacitor
Eli is voltage leads current by 90 degrees in an inductor. Ice is Current leads voltage by 90 degrees in a capacitor.

[Longbow]

Re: LC Resonant Circuit

We know it as "Eli" the "Ice" man. Where E = Voltage, I = Current, L = inductor, C = capacitor
Eli is voltage leads current by 90 degrees in an inductor. Ice is Current leads voltage by 90 degrees in a capacitor.

While this information is true, it does not clear up the OP's confusion. I think we are dealing with EE 101 where they teach you a lot of useless stuff and hope you learn something on the job.

I have a query on capacitor's charging and discharging behavior (pattern) in parallel LC resonant circuit.

The charge at any given time on the plates of a capacitor is calculated using the equation you refer to (natural logs) and assumes a resistor, capacitor, and voltage source. This equation finds the charge at any given moment, given a set of initial conditions. A charge/discharge graph shows charge vs time. These calculations are referred to as being in the "time domain".

However, when we talk about parallel LC resonance circuit, there the capacitor's charging and discharging is not exponential but sinusoidal.

You might have included some formulas for our amazement.

If you are asking what happens after connecting an inductance accross a charged capacitor, then those conditions will change the shape of the charge/discharge graph because you are inserting a reactance into the circuit which behaves differently than a simple resistor. Theoretically, the moment that L is inserted into the circuit, a diminishing AC current will circulate briefly between the 2 components. The value of L in Henries must be known, as well as the charge/discharge time domain formula for inductors. I'm fairly certain these calculations can all be done in the time domain.

In any case, if the time domain charge/discharge graph of a capacitor does indeed become sinusoidal in an LC circuit, (which we know to be true from frequency domain calculations), it is because the respective reactances of the two parts (at resonance) are mathematically equal but inverse, and therefore the exponential terms in the time domain charge equations cancel each other. (Assume a pure inductance, R=0.)

Don't ask me to prove this. You can use a calculator but not a computer to do the proof. And, I want it on my desk by Monday morning!

[keeney123]

Re: LC Resonant Circuit

I explained the LC circuit in this way hoping iamakda would take a interest and investigate further how these components behave under certain conditions.

[Longbow]

Re: LC Resonant Circuit

Very briefly stated, the reason for the difference in charging behavior noted above is as follows. The simple RC charging curve explained here:

https://www.youtube.com/watch?v=fdYLyPEBjYw
assumes a constant voltage source.

Time domain analysis of LC circuit will look different than the graphs shown in the video because the capacitor is NOT being charged by a constant voltage source (i.e. a battery), but instead it is being charged by an inductor. The proof is left to the reader.

The term "parallel LC resonance" is usually reserved for discussions in the frequency domain. So be careful not to mix up the domains.