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.

Answer 1

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