Why we know that the hypotenuse of the right triangle Z with two sides R and XL - XC is the total impedance of the circuit?
I meant that why we know for sure that |Z|=sqrt(R^2+(xL-xC)^2) is the impedance of the circuit not something like this |Z|= R^2+(xL-xC)^2 or something else. On what basis can we say that this value sqrt(R^2+(xL-xC)^2) is the impedance of the circuit?
Maybe, I miss some basic concepts here, please be kind.
Thanks for help.
I meant that why we know for sure that |Z|=sqrt(R^2+(xL-xC)^2) is the impedance of the circuit not something like this |Z|= R^2+(xL-xC)^2 or something else. On what basis can we say that this value sqrt(R^2+(xL-xC)^2) is the impedance of the circuit?
Maybe, I miss some basic concepts here, please be kind.
At present, I think I am familiar with the use of complex number in solving circuits. But I don't really how it work.
I want to know the the formula zL = jωL and zC = -j1/ωC are formed.
Here is my understanding about complex number: Complex numbers are really just pairs or numbers with a system of math attached to them that defines things like addition and multiplication in a manner that makes them useful to model two dimensional phenomenon.DC circuits can have variables like voltage represented by a single number like 10, 12, 15, etc, for 10v, 12v, 15v, etc. But AC circuits have voltages which must be represented by BOTH a voltage and a phase. These quantities are in general unrelated to each other so they have to be specified by two different numbers like 10 volts 90 degrees, or 12 volts with a phase of pi/2 radians. Note we are stuck having to use TWO numbers rather than just one to specify the voltage now.
With DC we have just say 10 volts, but with AC we have 10 volts at 90 degrees.
So with DC we have just "10", but with AC we have "10" and also "90" there.
I want to prove that.So for any real problem in the time domain the imaginary part cancels out or else we made a mistake.
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