Chad F.

asked • 06/14/17

A capacitor has a capacitive reactance of 50 ohms when connected to 60 hertz. What will be the capacitive reactance if the capacitor is connected to 1000 hertz?

Capacitive reactance

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Arturo O. answered • 06/14/17

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Xc = 1/(ωC)
 
C = 1/(Xcω)
 
ω = 2πf =  2π(60 Hz) ≅ 377.0 rad/s
 
C = 1/[(50)(377.0)] F = 5.305 x 10-5 F
 
At 1000 Hz,
 
ω = 2π(1000 Hz) ≅ 6283 rad/s
 
Xc = 1/(ωC) = 1/[(6283)(5.305 x 10-5)] ≅ 3.000 ohms
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Arturo O.

Another way to solve this without having to first find the capacitance:
 
Xc(ω2) / Xc(ω1) = [1/(ω2C)] / [1/(ω1C)] =  ω1/ω2 = f1/f2
 
Xc(ω2) = (f1/f2) Xc(ω1) = (60/1000) (50) ohms = 3 ohms
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06/14/17

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