Rms current in circuit with capacitor resistor and rms output

AI Thread Summary
The discussion revolves around calculating the rms current in a circuit consisting of a 39.5 uF capacitor and a 47.0 ohm resistor connected to a generator with an rms output of 25.2 V at 60.0 Hz. Participants are attempting to derive the correct rms current using various formulas, including those for impedance and reactance, but are struggling to connect the given values to the desired outcome. There is confusion regarding the use of inductance (L), which is not provided in the problem, leading to uncertainty in calculating impedance (Z). The correct approach involves using the impedance formula for the RC network and applying Ohm's law to find the current. The discussion highlights the importance of understanding complex numbers in electrical engineering, particularly the use of 'j' to represent the imaginary unit.
a_ferret
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Homework Statement



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)

Homework 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

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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Formulate the expression for Z, then you know that I = V/Z.
 
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
 
Calculate the impedance Z of the RC network.

Z = R + \frac{1}{j \omega C}

(true for this particular problem)

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

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

In general,

Z = \Re \{ Z \} + j \Im \{ Z \}

Use the Pythagorean Theorem to find the magnitude of Z.

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

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

i_{RMS} = \frac{v_{RMS}}{|Z|}
 
What is j for those equations?
 
a_ferret said:
What is j for those equations?
Here I used the symbol j to represent \sqrt{-1}. This is common in electrical engineering courses, since the symbol i is already taken, representing current.
 
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