Understanding a Concept: Seeking Deeper Answers

[Special One]

I have been trying to understand it but I couldn't
can anyone illustrate with deeper answer?

 

[tech99]

The LC network is in series with R, so work out its total reactance first.
As with resistors in parallel, reactances use the same formula, but with either + or - signs.
So 1/X = 1/XL - 1/Xc
1/X = 1/10 - 1/60
X = 10 x 60 / (10 -60) = 600/-50 = -12
In other words, -j12.
Now add this to R,
Z = R + X
Z = 50 - j12

 

[Special One]

But I still didn’t get how j appeared!?

 

[tech99]

If you have a reactance, rather than a resistance, you put j infront. It means that the current in the component is 90 degrees to the voltage.

 

[Special One]

Alright, thanks a lot bro

 

[berkeman]

But I still didn’t get how j appeared!?

https://en.wikipedia.org/wiki/Electrical_impedance#Complex_impedance

 

[anorlunda]

But I still didn’t get how j appeared!?

I sympathize. $L, X=\omega L, j\omega L, jX, \vec Z$ are all notations for the same thing. Why so many? Because practitioners find it convenient. You'll just have to learn them all and live with it.

 

[zoki85]

I have been trying to understand it but I couldn't
can anyone illustrate with deeper answer?

There are lot of threads on PF regarding application of phasors. Just scroll down to the bottom of this page to see some them.

 

[DaveE]

I would look at this video series if I were you. Start at the beginning of AC circuit analysis. If you jump right to the complex impedance lecture I think you'll stay confused.
https://www.khanacademy.org/science...-topic/ee-ac-analysis/v/ee-ac-analysis-intro1

 

[Special One]

I would look at this video series if I were you. Start at the beginning of AC circuit analysis. If you jump right to the complex impedance lecture I think you'll stay confused.
https://www.khanacademy.org/science...-topic/ee-ac-analysis/v/ee-ac-analysis-intro1

Thx mate,

 

[Babadag]

One could measure voltage and current with an a.c.ammetter. Then you'll get an average voltage named "rms" [root mean square].

Actually the alternative instant current [a.c.] value changes all the time very fast in a cyclic way.

From maxim to maxim [peak to peak] values the time is very short T=1/60=0.0167 sec[16.7 millisecond] or 1/50=0.02 sec.

An oscilloscope can measure that[See the link] and we can represent the measurement results on a paper so we get a sinusoidal wave.
https://en.wikipedia.org/wiki/Oscilloscope

If the voltage is applied on a [pure] resistance a current will pass through the resistance and the current wave will be the same as the voltage wave only at a different scale.

Not the same phenomenon occurs if instead of a resistance we have a coil that means an inductive reactance: the current wave will lag the voltage wave with 0.0041 sec[90o or π/2 radians].

If instead of resistance we have a capacitor the current will lead the voltage by 90o.

One may represent this wave on a circle and since α=ω.t changes with t always we may think the circle rotates with ω radians/sec. Let's sit on the circle plane [in the same way we stand on the rotated Earth and we think the Earth is fixed and does not rotate].Then v(t)=√2.Vrms. Let's represent -for our convenience- on a scale 1/√2.Then v(t)=Vrms=V.

The line representing the voltage or current in the above circle we call it phasor [and some time vector].

We may use for V the angle 0 since V.cos(o)=V.

If i(t) angle will be φ<>o then the actual part of the current will be I*cos(φ) and in case of pure resistance

when φ=0 i(t)=I.

I.sin(φ) it does not represent a real part of the current but a "parasite" one.

If we use the factor j=√-1 -which does not exist actually-we may assemble an imaginary expression j.sin(φ)

So we can consider y ordinate as imaginary one while abscissa x as the real [as voltage ].

i(φ)=I.cos(φ)+j.I.sin(φ)

If φ=0 i(φ)=I

If φ=-90o i(φ)=-j.I.sin(φ)

If φ=+90o i(φ)=+j.I.sin(φ)

If we multiply I^2 by R we get an actual power which we can measured with a wattmeter.

If we divide V by XL=2.π.f.L where f=supply system frequency and L the circuit inductance, or XC=1/(2.π.f.C) we get the current [IL or IC].But IL^2.XL [or IC^2.XC] it cannot be measured on a wattmeter. It is not a real power but a "reactive power".

If we combine a resistance and an inductance or capacitor we get a mixed current where tangent(φ)=XL/R [or XC/R].

 

[hutchphd]

Just for completeness someone should mention the term "complex number". That is what this phasor stuff really is and I think it may just be easier to learn rudimentary complex numbers and then this stuff is easy. I was taught using phasors from Sears and Zemansky and to this day do not know why. This is a general comment as well as for the OP because he/she seems at peace with it