A resistor, inductor, and a battery are arranged in a circuit. The circuit has an inductance of L = 1.8 H, and a resistance of 1.4 kΩ. Switc

Question

A resistor, inductor, and a battery are arranged in a circuit. The circuit has an inductance of L = 1.8 H, and a resistance of 1.4 kΩ. Switch S1 is suddenly closed at t = 0. Find the time needed for the current to reach a fraction f = 0.5 of its maximum value.

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Sigridomena 5 years 2021-08-22T03:20:26+00:00 1 Answers 119 views 0

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  1. Amity
    0
    2021-08-22T03:21:36+00:00
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    Answer:

         t = 8.9 10-3 s

    Explanation:

    The charge on an RL circuit is

              I = I₀ (1 – e^{-t/tau})

    Where tau is the circuit response time

               τ = L / R

               i / io = 1- e_{-t/\tau }

                0.5 = 1-e_{-t/\tau }

                 e_{-t/\tau } = 1 /0.5 = 0.5

               -t / τ = ln 0.5

                t = τ ln 0.5

                τ = L / R

                t = L / R ln 0.5

                t = 1.8 / 1.4 103 ln 0.5

                t = 8.9 10-3 s

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