Question

Derive an expression for the instantaneous voltage across the capacitor. Express your answer in terms of the variables C, R, I0, and t.

My previous answers that were incorrect: 1) VC=I0*Cos(omega*t)*R (Response was that the answer doesn't depend on (omega*t) 2)Vc=I0*Cos((1/RC)*t)*R (Response was Incorrect; Try Again; One attempt remaining You have found the voltage across the resistor. Note that the current and voltage across the capacitor are out of phase.)

Previous question info:

Part A) A 300 Ω resistor is connected in series with a 50 mH inductor. The voltage across the resistor is vR=(1.20V)cos(2500rad/s)t. Find the amplitude of the voltage across the inductor.

Part B) What should multiply the amplitude to obtain an expression for the instantaneous voltage vL across the inductor?

Part C) The current through a series combination of a capacitor C and resistor R is given by I0cos(ωt), where ω is chosen so that the reactance of the capacitor is equal to the resistance R. Derive an expression for ω.

Thank you

Answer 1

For the asked question we have to solve Part (C) of the previous question,

Given, a capacitor ( C ) and resistor ( R ) are in a series combination.

Current passing thorough them ( I ) =

We have also given a condition that the reactance of the capacitor is equal to the resistance R.

We know that the reactance of the capacitor ( ) = ,

Now using the given condition we have,

  

  

   ......( 1 )

For the instantaneous voltage across the capacitor,

Since, the capacitor and resistor are in series and the reactance of capacitor and resistance of resistor are equal.

So, the voltage across the capacitor will be equal to the voltage across the resistor.

Instantaneous voltage across the resistor ( ) =

putting the value of current,

putting the value of from equation ( 1 ),

  ,

We know that the voltage across the capacitor will be equal to the voltage across the resistor,

So, the instantaneous voltage across the capacitor ( ) =