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Statement of a problem № 10843

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The purpose of this problem is to show that the work W needed to establish a final current If in an inductor is W = 1/2 LI2f (Equation 22.10). In Section 22.8 we saw that the amount of work ∆W needed to change the current through an inductor by an amount ∆I is ∆W = LI(∆I), where L is the inductance. The drawing shows a graph of LI versus I. Notice that LI(∆I) is the area of the shaded vertical rectangle whose height is LI and whose width is ∆I. Use this fact to show that the total work W needed to establish a current If is W = 1/2 LI2f.




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