Ask Question
23 March, 01:30

A 5.6 V battery is connected in series with a 41 mH inductor, a 100 Ω resistor, and an open switch. At what time after the switch is closed (t=0) will the current in the circuit be equal to 12 mA?

+3
Answers (1)
  1. 23 March, 05:28
    0
    The current in a direct current resistor inductor circuit is given by:

    i (t) = (-ℰ/R) e^{-Rt/L} + ℰ/R

    Where i (t) is the current, t is time, ℰ is the battery's terminal voltage, R is the resistor's resistance, and L is the inductor's inductance.

    Given values:

    ℰ = 5.6V

    R = 100Ω

    L = 4.1*10⁻²H

    Plug in the values to get i (t):

    i (t) = - 0.056e^{-2440t} + 0.056

    We want to calculate when the current is 0.012A, i. e. find a time t when i (t) = 0.012A. So let us set i (t) equal to 0.012 and solve for t:

    -0.056e^{-2440t} + 0.056 = 0.012

    0.056e^{-2440t} = 0.044

    e^{-2440t} = 0.786

    -2440t = ㏑ (0.786)

    t = - ㏑ (0.786) / 2440

    t = 9.87*10⁻⁵s
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A 5.6 V battery is connected in series with a 41 mH inductor, a 100 Ω resistor, and an open switch. At what time after the switch is closed ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers