For an RL circuit with R = 37.84 Ω and L = 65.79 mH, how long does it take the current to reach 75% of its maximum value? ms
Question
For an RL circuit with R = 37.84 Ω and L = 65.79 mH, how long does it take the current to reach 75% of its maximum value? ms
Solution
In an RL circuit, the time it takes for the current to reach a certain percentage of its maximum value is given by the time constant, τ, which is L/R.
Step 1: Calculate the time constant, τ. τ = L/R = 65.79 x 10^-3 H / 37.84 Ω = 1.74 x 10^-3 s = 1.74 ms
Step 2: The formula to find the time it takes for the current to reach a certain percentage of its maximum value is given by t = -τ ln(1 - percentage).
Step 3: Substitute τ = 1.74 ms and the percentage = 75% = 0.75 into the formula. t = -1.74 ms ln(1 - 0.75) = 1.01 ms
So, it takes approximately 1.01 ms for the current to reach 75% of its maximum value.
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