# Impedance of capacitor and inductors

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

anorlunda
Staff Emeritus
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.

anorlunda
Staff Emeritus
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.

cnh1995
Homework Helper
Gold Member
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.

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.
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.

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.
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

cnh1995
Homework Helper
Gold Member
how do you set up the differential equations,
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.

anorlunda
Staff Emeritus
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.

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.
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.

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.
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

cnh1995
Homework Helper
Gold Member
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
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.

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.
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.

sophiecentaur