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Homework Help: RC circuit in a camera flash

  1. Jan 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider the following circuit in a camera flash where a light bulb is in series with a charged capacitor:
    a) Derive, but do not solve, the governing differential equation for the circuit. (Hint: treat the resistor and the light bulb as a single resistance.)
    b) Assume Rlight = 5 ohms If at time t = 0 the switch is closed, the solution to the differential equation from part a) states that a current will develop in the circuit which will light the bulb according to: i(t) = Q/RC*e^(-t/RC) where Q is the initial charge present on the capacitor. We want the capacitor to discharge quickly to produce a short flash for photography. If we want i(t) to fall to half its maximum value in 0.01 s and the capacitor has a value of 160 muF, what should R be?
    c) Calculate the value of the ratio of the instantaneous power dissipated in the resistor to the instantaneous power dissipated in the light bulb, i.e. Powerresistor/Powerlight.

    **Image can be found at http://www.chegg.com/homework-help/...ies-charged-capacitor-derive-solve-g-q3553019
    2. Relevant equations
    v=1/C integral idt

    3. The attempt at a solution
    For a)

    I got 0 = R*di/dt + i(t)/C
    I found an expression for total voltage and differentiated it w.r.t. time

    b) I plugged in numbers and got that R = 85.2 ohms (but this seems large???)


    1/2 = e^(-t/RC) -- R=Rt-Rl = 85.2 ohms

    for c)

    Presistor = i^2*Rr
    Plight = i^2*Rl

    Dividing, i^2 cancel so: Rr/Rl = 17.04???
  2. jcsd
  3. Jan 29, 2015 #2


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    Homework Helper

    It is correct. That circuit is not efficient!
  4. Jan 30, 2015 #3
    Thank you! Would the power ratio also be correct? I wasn't 100% that the i^2 would just cancel..
  5. Jan 30, 2015 #4


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    Homework Helper

    It is correct. The same current flows both through the resistor and bulb, so their square is also the same, and cancel :)
  6. Jan 30, 2015 #5
    Perfect! Thank you so much! :)
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