An L-R-C circuit has an inductance that 0.430 , a capacitance of 2.45×10−5 , and a resistance that R.

You are watching: What is the angular frequency of the circuit when r=0?

(A) What is the angular frequency the the circuit once

*
?Expressyour price in radians every second.

(B) What value must R have to provide a diminish in angular frequency that 6.00

*
contrasted to the worth calculated in part A?Express your answer in ohms.


Given:

Question Details

An L-R-C circuit has an inductance the 0.430 , a capacitance of 2.45×10−5 , and also a resistance the R.

(A) What is the angular frequency of the circuit as soon as

*
?Express your answer in radians per second.

(B) What value have to R have actually to provide a to decrease in angular frequency of 6.00

*
contrasted to the value calculated in part A?Express your answerin ohms.

*

The voltage equations because that the three circuit elements are :

(1)

*
(2)

*
*
*
(3)

In equation (3) , we have that

*
is the initial voltage on the capacitor i m sorry is a constant .

I will certainly assume existing flowing in the clockwise direction . This way we have voltage autumn in the clockwise

direction . Ns will amount voltage rises in the respond to clockwise direction . Follow to Kirchhoff's voltage law

the sum of these voltage rises is zero . Ns will begin the sum at the top of the resistor :

*
. Take it the derivative the this equation with respect to

*
, and we acquire :

*

. Divide this equation through by

*
, and also wecan create the differential

equation for the collection circuit together :

(4)

The auxilliary equation to fix this differential equation is :

.

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We deserve to solve this auxilliary equation making use of the quadratic formula :

*
.

The current and voltage in the collection RLC circuit oscilates once :

*
. We have the right to then write the auxilliary solution as :

*
(5)

Thecoefficient of

*
inequation (5) is the radian frequencythat us are looking for :