Frequency of an L-R-C Circuit
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Question “Frequency of an L-R-C Circuit”
An L-R-C circuit has an inductance of 0.430 , a capacitance of 2.45×10−5 , and a resistance of R.
A L-R-C circuit has an Inductance of 0.430, a Capitance of 2.45×10-5, and a Resistance of R.
(B) What value must be to provide a decrease of angular frequency at 6.00 as compared to Part A?
These are the voltage equations for each of the circuit elements:
I will assume that current flows in clockwise direction. This would mean that voltage drops are occurring in the clockwise direction.
direction I will add the voltage rises in counterclockwise direction. Kirchhoff’s voltage law
The sum of all these voltage rises equals zero. The sum will be calculated starting at the top of resistor
and you get:
and the differential can be written.
Equation for the series circuit as:
This is the auxilliary equation that solves this differential equation.
This auxilliary equation can be solved using the quadratic method:
as can be written.
inequation (5) is the radian frequencythat we are looking for :
has an angular frequency of (6) that is:
(I am actually using).
We get the following:
we get :
Substitute HTMLMediaTag23 for in this equation and you get:
rounding to six significant figures we have :
(B) Now, the angular frequency should be reduced to 6% of LC value
Now to Find R
So R=90.4 O
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