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An $R L$ circuit with $L=3.00 \mathrm{H}$ and an $R C$ circuit with $C=3.00 \mu \mathrm{F}$ have the same time constant. If the two circuits have the same resistance $R,(\mathrm{a})$ what is the value of $R$ and $(\mathrm{b})$ what is this common time constant?

a. 1000 \Omega

b. 0.003 s

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Cornell University

Numerade Educator

Hope College

University of Winnipeg

for part A were asked to find the value of an R in an R L circuit in an R C circuit if they have the exact same time. Constant. Okay, well, Tao then in both cases is going to be equal to each other. So it Tao in an RC circuit is equal to our C and an L C circuit is equal to hell over our therefore solving for are we want to know the resistance Mrs Part A. So it's indicated. A such resistance is equal to the square root of induct Inso over capacity. It's which we know both plugging those values. In this expression, we find that this is equal to one times 10 to the third owes or one killer oh, become box and it is their solution For part A for part B were asked to go ahead and find this common time constant so I can simply be done by using either our time see or l over are. So we'll just go ahead and use our time. See, carrying out this expression, we find that this time constant is equal to three times 10 to the minus three seconds. You can box it in as their solution for party. That's the conclusion of our question