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Calculate the resistance in an $R L$ circuit in which $L=2.50 \mathrm{H}$ and the current increases to 90.0$\%$ of its final value in 3.00 $\mathrm{s}$

1.92 \Omega

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Rutgers, The State University of New Jersey

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Hope College

University of Winnipeg

Okay, So, uh, to start off this problem, we take the ratio off current and time. Three seconds to maximum current. And so that will be Colonel. The type that at a time t is IMF over resistance times one minus exponent of dynasty over the time constant the maximum current issue ever are. And so those cancel And we want that to be 90% for T Recall Street. So let me just rearrange these things here. Minus t over. Towel will be quite one explain. I'm out of here, but I will be 0.1. Um, So, um, tea and we know is three seconds. So Tao will be long minus, Uh oh. No slog will just be minus three seconds over log 0.1. She's a negative number, so towel will be 1.30 seconds off the time. Constant. Therefore, since we know the time Constant is inducted over assistance from our is L over tower. And so we have is 2.500. Towel is 1.30 seconds, giving you a resistance of 1.92 homes