Optimizing Camera Flash Performance: The Role of RC Circuits

In summary, the conversation discusses a camera flash circuit consisting of a light bulb and a charged capacitor. The differential equation for the circuit is derived, and calculations are made to determine the value of R for the capacitor to discharge quickly. The ratio of the power dissipated in the resistor to the power dissipated in the light bulb is also calculated. The final result is that the circuit is not efficient, with a power ratio of 17.04.
  • #1
Lucille
31
0

Homework Statement


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/questions-and-answers/consider-following-circuit-camera-flash-light-bulb-series-charged-capacitor-derive-solve-g-q3553019

Homework Equations


v=iR
v=1/C integral idt
P=i^2*R

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?)

so:

1/2Q/RC=Q/RC*e^(-t/RC)
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?
 
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  • #2
It is correct. That circuit is not efficient!
 
  • #3
Thank you! Would the power ratio also be correct? I wasn't 100% that the i^2 would just cancel..
 
  • #4
It is correct. The same current flows both through the resistor and bulb, so their square is also the same, and cancel :)
 
  • #5
Perfect! Thank you so much! :)
 

1. What is an RC circuit in a camera flash?

An RC circuit in a camera flash is a type of electrical circuit that uses a resistor (R) and a capacitor (C) to control the flow of current and produce a flash of light in a camera. The resistor limits the amount of current flowing through the circuit, while the capacitor stores and releases electrical energy to produce the flash.

2. How does an RC circuit work in a camera flash?

When the camera's shutter button is pressed, an electrical signal is sent to the RC circuit. The capacitor charges up with electrical energy from the battery. Once the capacitor is fully charged, it releases all of its stored energy in a short burst, which causes the flash of light to occur. The resistor controls the rate at which the capacitor charges and discharges.

3. What is the purpose of using an RC circuit in a camera flash?

The purpose of using an RC circuit in a camera flash is to control the timing and intensity of the flash. By adjusting the values of the resistor and capacitor, the circuit can produce a longer or shorter flash and a brighter or dimmer flash. This allows for more control over the lighting in a photograph.

4. Can the RC circuit in a camera flash be adjusted or modified?

Yes, the RC circuit in a camera flash can be adjusted or modified by changing the values of the resistor and capacitor. This can be done by a camera technician or through DIY modifications, but it is important to note that altering the circuit may affect the camera's functionality and could potentially damage the equipment.

5. Are there any drawbacks to using an RC circuit in a camera flash?

One potential drawback of using an RC circuit in a camera flash is that it can take some time for the capacitor to recharge after each use. This means that the camera may not be able to take rapid consecutive photos with the flash. Additionally, if the values of the resistor and capacitor are not properly chosen, the flash may not produce the desired lighting effect in the photograph.

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