posted by .

A fully charged 90-µF capacitor is discharged through a 60-Ω resistor. How long will it take for the capacitor to lose 80% of its initial energy?

I know energy is given by E(t)=q(t)^2, but beyond that I really don't know how to solve this. Any suggestions are appreciated.

Thank you!

  • Physics -

    E~Q² =>
    ln0.2 =- 2•t/R•C
    t= - ln0.2• R•C/2 =- (-1.6) •60•90•10⁻⁶/2 =0.0043 s.

  • Physics -

    E = (1/2) c v^2
    c = 90 * 10^-6
    q = c v
    so dq/dt = c dv/dt = -i
    v = -i r = r c dv/dt
    dv/dt = (-1/rc) v

    v = Vi e^kt
    dv/dt = k Vi e^kt = (-1/rc)Vi e^kt
    k = -1/rc
    v = Vi e^-t/rc
    E = constant * v^2
    so v^2 at t = .8 v^2 at t = 0
    v at t = sqrt (.8) v at t = 0
    v at t = .64 Vi
    .64 = e^-(1/rc)t
    ln .64 = -.446 = -(1/rc) t

    t = .446 * 90 * 10^-6 * 60

  • misread -

    sqrt .2 not .8
    .04 = e^-(1/rc) t
    -3.22 = -(1/rc) t
    t = 3.22 * 90 * 10^-6 * 60

  • Physics -

    thank you!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A capacitor of capacitance C= 10mF, is charged using a battery of potential V, through a resistor of resistance R = 250 ohms. the charge of the capacitor is given by Q(t)=CV[1− e ^ (−t/RC)] Find an expression for the current …
  2. physics

    A 20.0 \mu F capacitor initially charged to 20.0 \mu C is discharged through a 1.90 k\Omega resistor. How long does it take to reduce the capacitor's charge to 5.00 \mu C?
  3. Physics

    How long will it take a charged 80-ìF capacitor to lose 20 percent of its initial energy when it is allowed to discharge through a 45 ohm resistor?
  4. Physics

    In a portable defibrillator, energy is stored in a capacitor charged to a high potential difference. The capacitor is discharged through the patient’s body in a short, high-powered pulse. a) The capacitor in a portable …
  5. physics

    A fully charged 98 uF capacitor is discharged through a 125 ohms resistor. How long will it take for the capacitor to lose 75% of its initial energy
  6. physics

    A resistor with 780 is connected to the plates of a charged capacitor with capacitance 4.32 . Just before the connection is made, the charge on the capacitor is 7.80 1)What is the energy initially stored in the capacitor?
  7. Physic II

    Suppose a capacitor having a capacitance of C fully charged to a voltage V and then discharged through a resistor R. Derive the equation (in terms of C,V,and R) that shows how long a time the capacitor will take to lose 45 % of its …
  8. Physics

    A 600W flashlamp fitted to a camera is operated by discharging a 10 000 uF capacitor through the lamp. The capacitor is charged initially from a 6V battery. Calculate A) the energy stores in the capacitor when fully charged B) the …
  9. Physics

    A 14.1 μF capacitor is charged to a potential of 45.0 V and then discharged through an 80.0 Ω resistor. (a) How long after discharge begins does it take for the capacitor to lose 90.0% of the following?
  10. Physics

    A charged capacitor,C=10e-6 F, with an initial stored energy of 3.5J, is discharged across a resistor, R. The charge on the capacitor drops to 40% of its maximum value in time, t=8.2s, from the instant the switch is closed (t=0). Find …

More Similar Questions