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

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

(A) What is the angular frequency of the circuit when

*
?Expressyour answer in radians per second.

(B) What value must R have to give a decrease in angular frequency of 6.00

*
compared to the value calculated in Part A?Express your answer in ohms.


Given:

Question Details

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

(A) What is the angular frequency of the circuit when

*
?Express your answer in radians per second.

(B) What value must R have to give a decrease in angular frequency of 6.00

*
compared to the value calculated in Part A?Express your answerin ohms.

*

The voltage equations for the three circuit elements are :

(1)

*
(2)

*
*
*
(3)

In equation (3) , we have that

*
is the initial voltage on the capacitor which is a continuous .

I will assume current flowing in the clockwise direction . This means we have voltage drops in the clockwise

direction . I will sum voltage rises in the counter clockwise direction . According to Kirchhoff's voltage law

the sum of these voltage rises is zero . I will start the sum at the top of the resistor :

*
. Take the derivative of this equation with respect to

*
, and we get :

*

. Divide this equation through by

*
, and wecan write the differential

equation for the series circuit as :

(4)

The auxilliary equation to solve this differential equation is :

.

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We can solve this auxilliary equation using the quadratic formula :

*
.

The current and voltage in the series RLC circuit oscilates when :

*
. We can then write the auxilliary solution as :

*
(5)

Thecoefficient of

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