How Do You Calculate Capacitance in a Series RC Circuit?

[SereneKi]

Homework Statement

Consider a series RC circuit with R = 151 Ω and an unknown capacitor C as shown below.


http://www.flickr.com/photos/67342906@N0…


The circuit is driven by an alternating electromotive force with εRMS = 174 V at a frequency of f = 7.70 Hz. The current in the circuit is IRMS = 0.310 A. Calculate the capacitance C.

Homework Equations

(1) I(rms)=V(source) / ( R+ (1/C))
(2) I(rms)=C x V(source) / ( 1+ RC)

The Attempt at a Solution

tried to plug them into equation (1) to get C but it didn't work

0.31 =174 / (151+ 1/C )

C=0.00244 F

 

[SereneKi]

http://www.flickr.com/photos/67342906@N07/8490253833/in/photostream

this should work

 

[gneill]

Homework Statement

Consider a series RC circuit with R = 151 Ω and an unknown capacitor C as shown below.


http://www.flickr.com/photos/67342906@N0…


The circuit is driven by an alternating electromotive force with εRMS = 174 V at a frequency of f = 7.70 Hz. The current in the circuit is IRMS = 0.310 A. Calculate the capacitance C.

Homework Equations

(1) I(rms)=V(source) / ( R+ (1/C))
(2) I(rms)=C x V(source) / ( 1+ RC)

The Attempt at a Solution

tried to plug them into equation (1) to get C but it didn't work

0.31 =174 / (151+ 1/C )

C=0.00244 F

Your Relevant Equations are not correct in that they are not handling the summation of resistance (of the resistor) and reactance (of the capacitor) properly; they should add in quadrature (square root of sum of squares, just like vector components). Also, the reactance should depend upon the frequency of the driving signal, which in this case is given as 7.70 Hz.

 

[SereneKi]

Your Relevant Equations are not correct in that they are not handling the summation of resistance (of the resistor) and reactance (of the capacitor) properly; they should add in quadrature (square root of sum of squares, just like vector components). Also, the reactance should depend upon the frequency of the driving signal, which in this case is given as 7.70 Hz.

So

Irms = sqrt( R^2 + (1/2(pi)fC)^2)

 

[gneill]

So

Irms = sqrt( R^2 + (1/2(pi)fC)^2)

Now you're missing the electric potential Remember you're writing Ohm's law, so I = E/Z, where here Z is the sum of resistance and reactance as you've calculated above.

 

[SereneKi]

Now you're missing the electric potential Remember you're writing Ohm's law, so I = E/Z, where here Z is the sum of resistance and reactance as you've calculated above.

So

Erms/Irms = sqrt( R^2 + (1/2(pi)fC)^2)

 

[gneill]

So

Erms/Irms = sqrt( R^2 + (1/2(pi)fC)^2)

Yes. Solve for C.