AC Circuits

  • Thread starter ayajek
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  • #1
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Homework Statement


A series RLC circuit is connected to a 60 Hz AC source which produces an amplitude of εmax=20 V. The circuit element values are R= 20 Ω, L= 20 mH, C= 150 μF.

Calculate the total impedance of the circuit.

Homework Equations


Xc=1/ωC
XL=ωL
Z=√(R^2 +(XL-Xc)^2)
tan φ = (XL-Xc)/R
ω=1/√LC
εmax=Imax*Z

The Attempt at a Solution


I started out with Z=√(R^2 +(XL-Xc)^2) , and to get XL and Xc I used ω=2*pi*f .
I got my XL and Xc marked wrong. It wasn't a calculation mistake, so am I approaching the answer incorrectly?
 

Answers and Replies

  • #2
Hesch
Gold Member
922
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Calculate the total impedance of the circuit.
am I approaching the answer incorrectly?
It seems that your approach is correct, though I don't like your sign conventions. Example:

tan φ = (XL-Xc)/R.

I'd rather write:

tan φ = (XL+Xc)/R , but the value of Xc is negative.

I don't know if you are familiar with complex calculations where Z could be calculated as

Z = R + jωL + 1/( jωC ) = R + jωL + ( -j / ( ωC ) ).
 
  • #3
255
80
Inductive reactance

Xl = 2pi f L

Capacitive reactance

Xc = 1 / (2pi f c)




If you can use complex numbers (makes this much simpler)

z = R + j(Xl - Xc)



So, for example if
Xl = 12 ohms
Xc = 17 ohms
R = 25 ohms

you would have

z = 25 - j5 ohms

(because 12-17 = -5)


and you can happily use ohms law to get the current

i = v / z
 
Last edited:

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