rms current in circuit with capacitor resistor and rms outputby a_ferret Tags: rms, rms current, rms voltage, root mean square 

#1
Nov1510, 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+(XlXc)^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 



#2
Nov1510, 11:10 PM

HW Helper
P: 6,213

Formulate the expression for Z, then you know that I = V/Z.




#3
Nov1510, 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 



#4
Nov1510, 11:38 PM

HW Helper
PF Gold
P: 1,842

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] 



#5
Nov1510, 11:43 PM

P: 3

What is j for those equations?



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