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Rms current in circuit with capacitor resistor and rms output

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a_ferret
#1
Nov15-10, 10:52 PM
P: 3
1. The problem statement, all variables and given/known data

A 39.5 uF capacitor is connected to a 47.0 ohm resistor and a generator whose rms output is 25.2 V at 60.0 Hz. Calculate the rms current in the circuit.
(also asks for voltage drop across resistor, capacitor and the phase angle for the circuit, but I mostly want to get the first one first)

2. Relevant equations

I=current, V=voltage, R=resistance, f=frequency

Irms=1/sqrt(2)*Imax
Irms=delta Vc, rms/Xc
Xc=1/(2pi*f*c)
delta Vc,rms=Irms*Xc

and then I start going in circles

Other formulas that might be appropriate:
Vmax=Imax*Z
Z=sqrt(R^2+(Xl-Xc)^2)
Xl=2pi*f*L
L=?? not given in this problem
Power average=Irms^2*R

3. The attempt at a solution
combining lots of these formulas trying to come up with the correct Vrms has proven unsuccessful. I came up with 17.819 A, .37515 A, .21739 A, none of which were right. None of them were successful and I don't remember or care to explain how I got them precisely because I wasn't confident in those anyway.
Overall I still haven't been able to link my given information directly to the answer I need
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rock.freak667
#2
Nov15-10, 11:10 PM
HW Helper
P: 6,202
Formulate the expression for Z, then you know that I = V/Z.
a_ferret
#3
Nov15-10, 11:17 PM
P: 3
but what do I use for L while setting it up for Z? I don't have it directly in the given information and I don't think I can derive it. Should I just use a default value like 1 or 0?

ps thanks for a response :D

collinsmark
#4
Nov15-10, 11:38 PM
HW Helper
PF Gold
collinsmark's Avatar
P: 1,953
Rms current in circuit with capacitor resistor and rms output

Calculate the impedance Z of the RC network.

[tex] Z = R + \frac{1}{j \omega C} [/tex]

(true for this particular problem)

[tex] Z = R +j \left( \frac{-1}{\omega C} \right)[/tex]

For this problem, the resistance is R, and the reactance is -1/(ωC).

In general,

[tex] Z = \Re \{ Z \} + j \Im \{ Z \} [/tex]

Use the Pythagorean Theorem to find the magnitude of Z.

[tex] |Z| = \sqrt{\left( \Re \{ Z \} \right)^2 + \left( \Im \{ Z \} \right)^2} [/tex]

And finally [the complex version of] Ohms law to find the current.

[tex] i_{RMS} = \frac{v_{RMS}}{|Z|} [/tex]
a_ferret
#5
Nov15-10, 11:43 PM
P: 3
What is j for those equations?
collinsmark
#6
Nov16-10, 12:19 AM
HW Helper
PF Gold
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P: 1,953
Quote Quote by a_ferret View Post
What is j for those equations?
Here I used the symbol j to represent [itex] \sqrt{-1}[/itex]. This is common in electrical engineering courses, since the symbol i is already taken, representing current.


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