# Capacitive reactance question

Discussion in 'Homework Help' started by metelskiy, Jan 21, 2011.

1. ### metelskiy Thread Starter Member

Oct 22, 2010
66
3
I have the following problem:
A 5 μF capacitor is connected across a voltage source = 170sin(377t) V.
What is capacitive reactance?
Here is my approach ($f$ is not given):
I know, to find capacitive reactance i use formula $X_C=\frac{1}{2\cdot\pi\cdot f\cdot C}$
So that would be $\frac{1}{2\cdot\Pi\cdot 0Hz\cdot 5uF}$ ? I don't even need to touch $V_s$?

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2. ### StayatHomeElectronics AAC Fanatic!

Sep 25, 2008
1,022
70
In generic terms a voltage source could also be written as

Vs = Vp sin(ωt)

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3. ### mbohuntr Active Member

Apr 6, 2009
413
32
Reactance is for AC voltage, therefore will have a frequency. 0hz will not work. Both inductors and capacitors will behave similar to a resistor at various frequencies, The capacitor offers less reactivity at higher frequency, and the inductor prefers lower frequencies. Things like radios, remotes and speakers use this theory to only respond to specific frequencies. When the capacitative reactance is equal to the inductive reactance, the circuit is said to be at resonance. The 377t seems like it might be time?? perhaps there is a frequency there...

Last edited: Jan 21, 2011
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4. ### Papabravo Expert

Feb 24, 2006
11,079
2,158
Did it escape your notice that
Code ( (Unknown Language)):
1.
2. 2∏*60 ≈ 377
3.
Code ( (Unknown Language)):
1.
2. 1 / (377)(5e-6) = ? Ohms
3.
BTW (1/0) would approach infinity so that cannot be the answer

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5. ### mbohuntr Active Member

Apr 6, 2009
413
32
That's good insight papa, I didn't look into the 377t, We were always given the frequency. I've never seen it written with a "t". I was thinking the t was for time, and 1/t = f.

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6. ### nathalie New Member

Jan 9, 2011
14
1
You need to use the angular frequency, ω which from the given equation is equal to 377.

Dont forget ω = 2 ∏f

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7. ### metelskiy Thread Starter Member

Oct 22, 2010
66
3
Papabravo, thanks for clearing me on this that $f=60Hz$
$X_C=\frac{1}{377\cdot 5uF}=1.8kohms$

On the same problem (A 5 μF capacitor is connected across a voltage source = 170Vsin(377t) what is the equation of current and there are multiple answers:

a. i = 0.32 sin(377t+90°)A
b. i = 0.32 sin(377t-90°)A
c. i = 0.5 sin(377t+90°)A
d. i = 0.5 sin(377t-90°)A
e. i = 0.5 sin(377t+180°)

But I don't get any of those answers. Since $I=\frac{V}{R}$
So $I=\frac{170Vsin(377t)}{1.8kohms}=94.4V$
What am I doing wrong?

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8. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
719
I'm unsure how you ended up with 0Hz for frequency.

170 is the amplitude, while 377t is frequency. The function will give you the amplitude and phase at time t

$2 \cdot \pi \cdot \omega = f$
$Z_c = \frac{1}{\omega \cdot C$

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9. ### metelskiy Thread Starter Member

Oct 22, 2010
66
3
Thanks I already figured out that $f=60Hz$, for some reason i didnt figure it out at first.

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10. ### Papabravo Expert

Feb 24, 2006
11,079
2,158
Obviously calculation is not your strong suit. Remember a uF is one one-millionth of a Farad.

(377 * 5e-6)^-1 = 1 / (377 * 5 * 10^-6) = 1 / (.001885) ≈ 531 Ohms

The actual impedance of the capacitor is a complex number which is 531 Ohms at an angle of -90°. You could also write 0 - j531

so you would have
Code ( (Unknown Language)):
1.
2. 170*sin(377t + 0°) / (531, -90° )
3. ≈ 0.32sin(377t + 90°)
4. That is
5. {170 / 531, 0° - (-90°)} = {0.32, +90°}
6.