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A 24 V battery is connected in series with a resistor and an inductor, with $R=8.0 \Omega$ and $L=4.0 \mathrm{H}$ , respectively. Find the energy stored in the inductor (a) when the current reaches its maximum value and (b) one time constant after the switch is closed.

a. 18 \mathrm{J}

b. 7.2 \mathrm{J}

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Cornell University

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Hope College

Okay, so we know that, uh, energy was given by 1/2. Hell, I squared hum, and the eye is new over. Our eyes are absolutely are so for for when current is maximum So maximum energy energy at maximum current is 1/2 times l times have you ever are are sort of are squared So this is the maximum current. Ah, so this is 1/2 times floor Henry's times 24 volts over eight homes. Use your three m's quality squared nine times two is 18. So that's 18 Jules for a number for part B, you want energy at one time constant. So I will be 10.62 or 62.2% of maximum, um, en masse over our So in this case, you have energy equals 1/2 times out. Times 0.62. Uh, looks 0.62 absalon over our square. Say see, from here to here, the only difference is this. Ahh factor of 0.632 square. So most play 18 by 180.62 squared and you get almost 7.2 jewels. That's