How Does Capacitance Affect Current in an AC Circuit?

[deenuh20]

Homework Statement

An ac generator with a frequency of F=25 Hz and an rms voltage of 15 V is connected to a C=32 µF capacitor. Assume that the generator produces a sinusoidal waveform.

(a) What is the maximum current in the circuit? mA

(b) What is the current in the circuit when the voltage across the capacitor is 7.5 V and increasing?
(c) What is the current in the circuit when the voltage across the capacitor is 7.5 V and decreasing?

Homework Equations

Irms= Vrms*Xc

Irms= [1/(2)^(1/2)]* Imax

The Attempt at a Solution

part (a): already figured it out using Irms= Vrms*Xc and got the answer of 106.629 mA, which is correct.

part (b) and (c): I tried using the Irms= Vrms*Xc equation and plugging in 7.5 Volts as V and solving for I, since I already have Xc which is just 1/(angular freq. * Capacitance)

 

[robb_]

What again is ohms law?

 

[deenuh20]

Ohm's Law is V=IR

The equation I was using above (Irms= Vrms*Xc ), is analagous to Ohm's law (well, according to my textbook), just rearranged.

*Edit*

I meant to type Irms= Vrms/Xc, not multiplied in my previous 2 posts.

 

[robb_]

Ah, okay its $$V = I X$$. units look okay now
But what again is X and how might I calculate it?

*edit*
sorry, i see you got it, those formulae disturb me though

 

[deenuh20]

I solved the equation!

X is just 1/(2*pi*frequency*capacitance).

To figure the problem out, I used the equation to find the instanteous voltage on a capacitator:

V=Vmax*sin(theta-90degrees).

To find theta, I just found the Vmax by using the Vrms (15V) and multiplying it by 2^(0.5). Then, I plugged in for the equation:

7.5=Vmax*sin(theta) and solved for theta.

Then, I took theta and plugged it into

Current=Current (max) *sin (theta)