In section 32.5 on page 859 in the paragraph above equation 32.16 it says
Often, when analyzing AC circuits, the only things we are interested in are the amplitudes ....
In that one sentence there are several bugs.
I'm not even counting the fact that it says "potential difference" when it should say "voltage"; see item #60.
First of all, the sentence in question is contradicted by the very next paragraph, where it becomes clear that we are interested in the phase, not just the amplitude.
Secondly, one is hardly ever interested in a pure sine wave for its own sake. Usually the signal is a superposition of many sine waves.
Thirdly, saying "sometimes" is not much of a motivation and not much of an explanation. The key idea here is that for _LINEAR_ circuits we can Fourier-analyze the signal and then understand it one frequency at a time. To motivate this and explain it, you need to say something about what a linear circuit is, and why it is important. This will require a few paragraphs; a highly condensed version of the story can be found here:
https://www.av8n.com/physics/linear-circuit-intro.htm
Fourthly, nobody in their right mind calculates using amplitude and phase. Instead they use phasor components. Phasors are a linear function of the input, whereas amplitude and phase are not.
Equation 32.16 is OK as far as it goes, but it needs a more serious explanation of what it's good for ... and what it's not good for.
In section 32.5 on page 859 in the paragraph above equation 32.16 it says
In that one sentence there are several bugs.
I'm not even counting the fact that it says "potential difference" when it should say "voltage"; see item #60.
First of all, the sentence in question is contradicted by the very next paragraph, where it becomes clear that we are interested in the phase, not just the amplitude.
Secondly, one is hardly ever interested in a pure sine wave for its own sake. Usually the signal is a superposition of many sine waves.
Thirdly, saying "sometimes" is not much of a motivation and not much of an explanation. The key idea here is that for _LINEAR_ circuits we can Fourier-analyze the signal and then understand it one frequency at a time. To motivate this and explain it, you need to say something about what a linear circuit is, and why it is important. This will require a few paragraphs; a highly condensed version of the story can be found here: https://www.av8n.com/physics/linear-circuit-intro.htm
Fourthly, nobody in their right mind calculates using amplitude and phase. Instead they use phasor components. Phasors are a linear function of the input, whereas amplitude and phase are not.
Equation 32.16 is OK as far as it goes, but it needs a more serious explanation of what it's good for ... and what it's not good for.