AC Circuit and Thevenin's theorem

  • #1
archaic
688
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Homework Statement


I'm asked to find the thevenin equivalent circuit, the load being ##R_1##
1542811172-2018-11-21-15-33-42.jpg

##e(t)=E_0\cos{(\omega t)}##
##R_1=1k\Omega \ R_2=R_3=1k\Omega##
##C=220nF \ f = 250Hz \ E_0=10V##

Homework Equations

The Attempt at a Solution


##Z_{th} = Z_{R_2}//(Z_c+Z_{R_3}) = \frac{R_2R_3C\omega-jR_2}{(R_2+R_3)C\omega -j}##
As for ##E_{th}## :
##\overline{\rm E_{th}} = \frac{Z_c+Z_{R_3}}{Z_c+Z_{R_2}+Z_{R_3}}\overline{\rm e} = \frac{R_3-j\frac{1}{C\omega}}{R_2+R_3-j\frac{1}{C\omega}} \overline{\rm e}##
First of all, are the starter results correct?
Second, how should I proceed after this, replace the variables with their actual values then substitute ##\overline{\rm e}## with ##E_0e^{\omega t}##, develop and get the real part?
 

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  • #2
archaic said:
First of all, are the starter results correct?
Looks good so far.
archaic said:
Second, how should I proceed after this, replace the variables with their actual values then substitute ##\overline{\rm e}## with ##E_0e^{\omega t}##, develop and get the real part?
Nah. The real part alone does not fully describe the network, so it would no longer be a Thevenin equivalent.

Find the magnitude and angle for your ##E_{th}## above and write it in the form ##E \cos(\omega t + \phi)##, and for ##Z_{th}## you might just leave it as an impedance in complex form, or, for extra points, show the impedance can be represented by the series connection of a resistor and one reactive component.
 
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  • #3
gneill said:
Looks good so far.

Nah. The real part alone does not fully describe the network, so it would no longer be a Thevenin equivalent.

Find the magnitude and angle for your ##E_{th}## above and write it in the form ##E \cos(\omega t + \phi)##, and for ##Z_{th}## you might just leave it as an impedance in complex form, or, for extra points, show the impedance can be represented by the series connection of a resistor and one reactive component.
Won't the magnitude of ##Z_{th}## be equal to ##R_{th}##?
 
  • #4
archaic said:
Won't the magnitude of ##Z_{th}## be equal to ##R_{th}##?
No. Impedance has real and imaginary parts. The real part corresponds to resistance, the imaginary part to reactance.

You can assign the real part to a resistor. The imaginary part you need to decide whether an inductor or a capacitor will fill the bill.
 
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