Physics- Circuits

At time t=0, a potential difference of 475 V is applied to a coil with an inductance L=0.642 H and a resistance R=36 ohms. How long does it take to reach 20 percent of maximum energy in the inductor?

  1. 👍 0
  2. 👎 0
  3. 👁 88
asked by Bobby
  1. V = L di/dt + i R
    i is of form i = (V/R)(1 - e^-kt)
    di/dt = (V/R)k e^-kt
    so
    V = (L V/R )k e^-kt +R(V/R)(1-e^-kt)
    1 = (L/R)k e^-kt + 1 - e^-kt
    0 = (L/R)k -1
    so
    k = R/L
    so
    i = (V/R) (1 - e^-(R/L) t )
    U = energy stored in magnetic field of inductor = (1/2) L i^2
    U = (1/2) L V^2/R^2 (1-e^-kt)^2
    this is maximum when i is maximum which is as t--> oo
    U max = (1/2)L(V/R)^2
    .2 Umax = 0.1 L(V/R)^2
    so when is that true?
    0.1 L(V/R)^2 = .5 L(V/R)^2 (1-e^-kt)^2
    .2 = (1-e^-kt)^2
    1 - e^-kt = sqrt .2 = .447
    e^-kt = 1-.447 = .552786
    1/e^kt = .552786
    e^kt = 1.81
    kt = ln 1.81 = .593
    t = .593/k
    but k = R/L = 36/.642
    so
    t = .593 (.642/36) = .0106 s

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. Thanks!

    1. 👍 0
    2. 👎 0
    posted by Bobby
  3. You are welcome but ALWAYS check my arithmetic :)

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A video game console operates potential difference of 12.00 V as shown in fig. The potential difference supplied by the power receptacle is 120 V AC. A transformer is used to convert one voltage to the other. If the secondary coil

    asked by Learner on January 14, 2018
  2. physics

    In the circuit we have E=48V, R=6 ohm and L=4H. We close the switch at the instant t=0, the current I in the circuit grows from zero to its maximum value Io, and the permanent phase is established. A) determine the value of Io. B)

    asked by vicky on December 6, 2016
  3. science

    The potential difference measured across a coil is 20 V when a direct current of 2 A is passed through it. With an alternating current of 2 A at 40 Hz, the p.d. across the coil is 140 V. If the coil is connected to a 230 V, 50 Hz

    asked by mpho on July 29, 2015
  4. physics- magnetism

    A step-up transformer used in a car has a potential difference of 10 V across the primary coil with 12 turns. What is the current in the secondary coil of resistance 2.5 Ω if the number of turns in the secondary coil is 54 turns?

    asked by marjean on September 14, 2016
  5. Physics Capacitance

    Three uncharged capacitors, X, Y, Z, each with capacitance of 12uF each are connected A---------[X]------[Y/Z]-----------B *Y&Z is parallel to each other* A potential difference of 9.0V is applied between points A and B. Explain

    asked by Ariana on April 25, 2015
  6. Physics pls help

    Consider two single turn coils labeled 1 and 2 that are positioned close to each other. The switch S has been open for a long time. If the switch is now closed and the current through coil 1 is in the direction shown and

    asked by aaka on December 16, 2013
  7. Physics Help pls

    Consider two single turn coils labeled 1 and 2 that are positioned close to each other. The switch S has been open for a long time. If the switch is now closed and the current through coil 1 is in the direction shown and

    asked by aaka on December 16, 2013
  8. PHYSICS

    Consider two single turn coils labeled 1 and 2 that are positioned close to each other. The switch S has been open for a long time. If the switch is now closed and the current through coil 1 is in the direction shown and

    asked by aaka on December 15, 2013
  9. Physics

    A transformer consists of 275 primary windings and 834 secondary windings. If the potential difference across the primary coil is 25 V, (a) What is the voltage across the secondary coil? (b) what is the effective load resistance

    asked by J on March 18, 2008
  10. Physics

    A transformer consists of 275 primary windings and 834 secondary windings. If the potential difference across the primary coil is 25 V, (a) What is the voltage across the secondary coil? (b) what is the effective load resistance

    asked by J on March 18, 2008

More Similar Questions