Question

A series RLC circuit consists of a 56.0 ? resistor, a 3.80 mH inductor, and a 400 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 4.10 V.

Part A

What is the instantaneous emf E when i =I?

Express your answer with the appropriate units.

0V

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Part B

What is the instantaneous emf E when i =0A and is decreasing?

Express your answer with the appropriate units.

3.02 V

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Correct

Part C

What is the instantaneous emf E when i =?I?

Express your answer with the appropriate units.

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Answer 1

Given:

A series RLC circuit consists of a 56.0 ? resistor, a 3.80 mH inductor, and a 400 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 4.10 V.

Part A

What is the instantaneous emf E when i =I?

Express your answer with the appropriate units.

0V

SubmitHintsMy AnswersGive UpReview Part

Incorrect; Try Again; 5 attempts remaining

Part B

What is the instantaneous emf E when i =0A and is decreasing?

Express your answer with the appropriate units.

3.02 V

SubmitHintsMy AnswersGive UpReview Part

Correct

Part C

What is the instantaneous emf E when i =?I?

Express your answer with the appropriate units.

We are given in the series   circuit that , , and   .

The peak sinusoidal voltage is    and the frequency is ---   .

We then have the radian frequency is ---    . We can then write the source voltage is :

(1) . The rms voltage is then    .

We can say the magnitude of the rms voltage is ---    .

The inductive reactance is ---   .

The capacitive reactance is --- .

We then have the impedance of the series circuit is :

The magnitude of the impedance is :

The phase angle of the impedance is --- .

We can thus write the complex number    in polar form :

   .

We then have the phasor current is :

.We can then find the amplitude of the current in the time domain :

   ===>

   ( Where   is the rms current )

We then have the current in the time domain is :

   (2)

for the input voltage of :

(1)   

A) First , they want to know what the input instantaneous emf is when the instantaneous current is equal to the rms .

That is they want   when    . From equation (2) , we thus solve :

   ===> ( Note in this calculation that the angle in degrees must be converted to radians ) :

  ===>

===>

  .

We can then substitute   into equation (1) to find the emf when   :

   --- SOLUTION ( Your calculator must be in radians mode to do this calculation )

B) They want     when    and decreasing . This happens when :

   ===>

  ===>

   ===>

. We can thus find the emf when by substituting into equation (1) :

  --- SOLUTION .

C) The want the input emf when   .

This happens when :

  ===>

  ===>

  .

We can thus find when   by substituting into equation (1) :

   --- SOLUTION .