(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A resistor [tex]R[/tex] is connected in series with an inductor [tex]L[/tex]. The battery is connected at time [tex]t = 0[/tex]. How much of this energy after 2 seconds is stored in the magnetic field of the inductor?

2. Relevant equations

[tex]U_{L}=\frac{1}{2}Li^{2}[/tex]

[tex]i(t)=i_{0}(1-e^{\frac{-t}{\tau}})[/tex]

3. The attempt at a solution

I know that you're supposed to square [tex]i(t)[/tex] and then multiply by [tex]\frac{L}{2}[/tex]. However, when I looked at the solution they have it as:

[tex]U=\frac{L}{2}\int{i(t)^{2}dt[/tex]

why do you need to multiply by the integral of current squared instead of just the current squared? what is the final answer telling me if i multiply by the current squared versus the integral of the current squared?

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# Homework Help: Question about inductors

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