# Impedance of capacitor and inductors

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1. Mar 26, 2016

### Puglife

I do not understand how to solve capacitors and inductors with impedance. I do not even know what it is that they use it to solve for. My understanding is that the define the source as a sinusoid using the complex exponential form, and that all voltages and amperage are now also complex exponential.

I do not, however, know how to solve them, nor do I know what I am solving for? so I need to know, what is it used to solve for, how do you solve it using that, and why use that method?

Also, any proofs would be extremely helpful for me conceptualizing it.

Thank you all

2. Mar 26, 2016

### Staff: Mentor

3. Mar 26, 2016

### Puglife

That said you need to use differential equations in order to calculate the instantaneous power at a given point, but what I am asking is how to use the complex exponential wave in order to calculate that for a capacitor and inductor, it is a different thing.

If you model your source as a complex exponential wave, then everything else is also modeled as that, and you can somehow solve for all of the instantanious voltage and amperage at given points.

What I dont understand is how that is possible, how to do that, or exactly how any of those equations got derived.

4. Mar 26, 2016

### Staff: Mentor

Can you solve them using $\cos{\omega t}$?
Do you understand that $e^{-j\omega t}$ is equivalent to $\cos{\omega t}$?

It sounds like your difficulties are not related to electricity, but rather to lack of practice with some needed algebra/calculus identities.

5. Mar 26, 2016

### cnh1995

Inductor and capacitor are "energy storing" elements. When you have only resistors in circuit, KVL equation for that circuit is a simple algebraic equation. When you have inductor or capacitor in the circuit, KVL becomes a differential (integro-differential) equation. Solving the differential equation, you can get the voltage across or current through those elements. For ac circuit analysis, phasor technique is used which is simpler compared to the DEs.

6. Mar 26, 2016

### Puglife

I do not know how to model the equations, and what to solve for, I am ok with my algebra and differential equations, but I have absolutely no idea how to set up the equations, nor where they get them from.

7. Mar 26, 2016

### Puglife

how do you set up the differential equations, or the phasor technique for it, is their any way you can supply sample calculations, as well as how those equations where derived (such as proofs).

Thank you all, you guys have been super helpful

8. Mar 26, 2016

### cnh1995

You need to know the i-v relations for inductor and capacitor. For example, voltage across inductor is Ldi/dt and voltage across capacitor is (1/C)∫idt. These are derived from the fundamental behavior of these elements.

9. Mar 26, 2016

### Staff: Mentor

Have you studied Ohm's Law? Do you have practice with DC circuit analysis?

The techniques (such as Kirchoffs Laws) are the same, but instead of $R=V/I$ for a resistor, you have $I=C\frac{dV}{dt}$ for a capacitor, and $V=L\frac{dI}{dt}$ for an inductor.

10. Mar 26, 2016

### Puglife

oh, ok, thats not too bad at all. Now all I need to know if how to use the complex exponential to solve it without the use of calculus, because alot of what they say in the book references directly that.

11. Mar 26, 2016

### Puglife

Also, it would be extremely helpful to know how those differential equations where derived, weather though experimentation, or though math, just so that I can better conceptualize it.

Thanks a ton

12. Mar 26, 2016

### cnh1995

Inductor opposes sudden change in current through it by inducing a back-emf proportional to the rate of change of current. Hence, voltage across it is Ldi/dt. Capacitor voltage is simply charge/capaticance i.e. q/C.
Since, q=∫idt, voltage across capacitor becomes,
V=1/C∫i dt. You should refer a good physics book for studying these circuits. Start with dc analysis so that you'll get comfortable with the DEs.

13. Mar 26, 2016

### Puglife

ok, thank you, now all I need to know if how to use the complex exponential to solve it without the use of calculus, because alot of what they say in the book references directly that.

14. Mar 27, 2016

### sophiecentaur

Is there any reason why you can't use a standard text book to find this information? Specific questions on PF will usually get a useful answer but it seems a bit unreasonable, to me, to expect a whole personalised course to be supplied by PF.
There are so many adequate text books available for this sort of thing - some are even available in line, for free.