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Help using complex numbers to work out LRC circuits ???

I am trying to understand XLR circuits and the use of complex numbers
to find solutions. I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j – 159j
Z = 50 – 96.2j or [email protected]

Suppose that I wanted to find the voltage drops across L, R, and C
when the power source is at .707V or 1@45 or .707 + .707j .

I = V/Z or
I = 1@45 / [email protected] = [email protected] or -.0027+.0087j
Taking the real part of -.0027+.0087j means that when the voltage
source is at .707 volts, the current through L, R, and C is at -.0027
amps.

The voltage across R:
(50@0) * ([email protected]) = [email protected] or -.138 + .438j
Taking the real part of -.138 + .438j means that when the voltage
source is at .707 volts, the voltage across R is at -.138 volts.

The voltage across L:
(62.8@90) * ([email protected]) = [email protected] or -.550 - .173j
Taking the real part of -.550 - .173j means that when the voltage
source is at .707 volts, the voltage across L is at -.550 volts.

The voltage across C:
(159@-90) * ([email protected]) = [email protected] or 1.394 + .440j
Taking the real part of 1.394 + .440j means that when the voltage
source is at .707 volts, the voltage across L is at 1.394 volts.
 
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No, it doesn't.  In standard scientific notation, the lower case 'm'
stands for 1/1000, not 1/1000000.

In order to eliminate confusion you should either use the symbol 'µ'
or spell out 'microhenry' if that's what you mean.

JF- Hide quoted text -

- Show quoted text -

I didn't know how to generate the "mu" character and even if I figured
it out I was afraid it wouldn't show up correctly on everyone's
computer so I used m for micro forgetting that m stands for milli like
ma in milli amps. I will spell it out in the furure to avoid any
confusion.

What about the rest of the math that follows ?????????????
 
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