Re: resistance in an LRC circuit used to calculate time constant

• To: tesla-at-pupman-dot-com
• Subject: Re: resistance in an LRC circuit used to calculate time constant
• From: "Malcolm Watts" <malcolm.watts-at-wnp.ac.nz> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
• Date: Mon, 13 Mar 2000 16:30:22 -0700
• Approved: twftesla-at-uswest-dot-net
• Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Hi Alfred,

> Original Poster: "Alfred C. Erpel" <alfred-at-erpel-dot-com> 
> 
> Hello,
>  
>  
>     An LRC circuit has three components of resistance; the internal
resistance
> of the inductor, the internal resistance of the capacitor, and resistance in
> the wiring connecting the inductor and capacitor.
> The resonant frequency of this LRC circuit is 1 / [2 * PI * SQRT(L * C)]
> regardless of the total resistance in the circuit.

Not strictly true.  In fact it is 1/[2*PI*SQRT{L*C + (R^2/4L^2)}]  or 
something pretty close. R has to be factored in because... consider 
the case where it is very large for instance.
  
> a)   The time constant of a capacitor is C * R.
> b)   The time constant of an inductor is L / R.

Both of those assume that R is present in the circuit. 
  
>     In the context of this resonant circuit, when you calculate the time
> constants of each device, how do you figure R?  Is R just the resistance
> internal to the device (inductor or capacitor) or do you add up the total
R for
> the circuit (all three components) to determine R for the equations
above? How
> do you account for the R in the circuit external to both devices?

R is simply the ESR (effective series resistance) of the resonant 
circuit and encompasses all circuit resistances suitably modelled as 
a single resistor.   Note that you can derive the value of Q required 
for critical damping from the formula given above (turns out to be 
0.5).

Regards,
Malcolm

• Prev: Re: Ultraviolet light from brush discharge.
• Next: Re: Interesting Skin Depth Data
• Index(es):
  • Main
  • Thread