The ratio of a sinusoidal voltage to a sinusoidal current is called impedance. Impedance is a generalization of the concept of resistance $(v/i)$. We derive the impedance of a resistor, inductor, and capacitor. The impedance of the inductor and capacitor includes a term for frequency, since the ratio of $(v/i)$ for these components depends on frequency.

Created by Willy McAllister.

Learner aandres on Khan Academy asked this relevant question about the Impedance video,

The part between 2:28 and 3:45 seems a circular reasoning to me. At 2:28 v = i*R. Then after some steps we get that, indeed, R = v/i.
(I mean we would get that no matter how i is defined, it does not matter that we used e^jwt in this case, it would work for any other kind of i as well.)

Yes. The discussion of the resistor is circular. It’s just two forms of Ohm’s Law, and it is valid for any form of i. This is intended to emphasize the perspective of Ohm’s Law as the ratio of v to i. It helps set up what comes next for L and C.

When we consider L and C, AND we assume the current or voltage is a complex exponential, the concept of Impedance emerges. It applies to L, C, and R. The R case is what you already know (Ohm’s Law) so it seems super simple.