Calculate Magnitude of Impedance for RLC Circuit

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SUMMARY

The discussion focuses on calculating the magnitude of impedance in an RLC circuit, specifically incorporating series resistance (Rx) into the impedance formula. The user references the impedance of a similar circuit (Z_a) and debates whether to use the formula Z = Rx + Z_a or Z = (Rx^2 + ?)^0.5. The process involves combining resistive and inductive components into an equivalent series impedance (Z1), then calculating the parallel impedance with a capacitor (Z2), and finally summing Rx with Z2 to derive the total impedance. The magnitude is determined using the formula sqrt(real^2 + img^2).

PREREQUISITES
  • Understanding of RLC circuit theory
  • Familiarity with complex impedance calculations
  • Knowledge of series and parallel circuit configurations
  • Proficiency in algebraic manipulation of complex numbers
NEXT STEPS
  • Study the derivation of impedance formulas for RLC circuits
  • Learn about complex number operations in electrical engineering
  • Research the effects of series resistance on phase angle in RLC circuits
  • Explore simulation tools for RLC circuit analysis, such as LTspice or Multisim
USEFUL FOR

Electrical engineers, students studying circuit theory, and anyone involved in analyzing or designing RLC circuits will benefit from this discussion.

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I need help calculating the magnitude of the impedance for a RLC circuit shown below. See the attached schematic.

I found the impedance magnitude of a similar circuit here:
Impedance Formulas

...see the 4th circuit from the bottom (let's call its impedance Z_a).

Unfortunately, I do not know how to include the series resistance Rx into this formula.
The problem I am having is whether to use the formula:
Z = Rx + Z_a
...or
Z = (Rx^2 + ?)^0.5

Also, I am not sure whether the value of the Rx will alter the phase angle between current and voltage of this circuit?
 

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First lump R and L into an equivalent series impedance, call it Z1, that will be a complex number: Z1 = R+jwL

So now you have an impedance Z1 in parallel with C.

Next, lump the equivalent series impedance found above with the capacitor in parallel into a new equivalent impedance Z2, remembering that the complex impedance of a capacitor is 1/(jwC): Z2 = (Z1 * (1/(jwC)))/(Z1 + 1/(jwc))

The last lumping is to combine Rx and Z2 as series impedances: Rx + Z2. It will help to get Z2 in terms of a real and complex part (manipulate the thing algebraically) so that you can just add Rx to the real part of Z2.

Now you can simplify this complex impedance to get a real and a complex term. Now you have the real and imaginary parts of the total circuit, and you use the magnitude formula sqrt(real^2 + img^2) to get the magnitude.
 

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