Impedance of Parallel Circuit

NullSpace0

A 1000 ohm resistor, 500 picofarad capacitor, and 2 millihenry inductor are all conducted in parallel. What is the impedance if the frequency is 10 kilocycles per second? 10 megacycles per sec? At what frequency is the absolute value of impedance the greatest?

I know I start by considering admittances since those add in parallel. I will end up with a complex number. Can I take its modulus and then the reciprocal? Or do I take the reciprocal to get impedance and then take the modulus? Or do I take the reciprocal to get impedance and leave it as the complex number?

Simon Bridge

You have a complex admittance.
The complex impedance is the reciprocal of the complex admittance
"Impedence" and "complex impedance" can be used interchangeably: you'll have to use the context of your classes to decide if the modulus is expected or not (that's how I'd interpret it.)

note; if ##y=a+jb##
then, using ##|z|=|1/y|## (i.e. reciprocal then modulus):$$z=1/y = 1/(a+jb) = (a-jb)/(a^2-b^2)\Rightarrow |z| = \sqrt{a^2+b^2}/(a^2-b^2)$$... something like that - what happens if you do it in the other order (i.e. modulus then reciprocal). Is ##|1/y|=1/|y|##)?

See:
http://en.wikipedia.org/wiki/Electrical_impedance

NullSpace0

Ahah! I was certainly wrong to think I could do the modulus and then take the reciprocal, that would give something like sqrt(a^2+b^2), and it would ignore the denominator that you got in the modulus of z itself.

So if I were to take the modulus, it should ALWAYS be after I've gotten all the way to the end of the problem in complex numbers?

Simon Bridge

It usually works out simpler that way anyhow.