Integrated Concept Problem: Calculating Capacitor Size—Strobe Lights · Physics Playground

Example 21.6 from College Physics, 21.6 DC Circuits Containing Resistors and Capacitors

Integrated Concept Problem: Calculating Capacitor Size—Strobe Lights

High-speed flash photography was pioneered by Doc Edgerton in the 1930s, while he was a professor of electrical engineering at MIT. You might have seen examples of his work in the amazing shots of hummingbirds in motion, a drop of milk splattering on a table, or a bullet penetrating an apple (see Figure 21.40). To stop the motion and capture these pictures, one needs a high-intensity, very short pulsed flash, as mentioned earlier in this module.

Suppose one wished to capture the picture of a bullet (moving at $5.0 \times 10^{2} m/s$ ) that was passing through an apple. The duration of the flash is related to the $RC$ time constant, $τ$ . What size capacitor would one need in the $RC$ circuit to succeed, if the resistance of the flash tube was $10.0 Ω$ ? Assume the apple is a sphere with a diameter of $8.0 \times 10^{–2} m.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We begin by identifying the physical principles involved. This example deals with the strobe light, as discussed above. Figure 21.39 shows the circuit for this probe. The characteristic time $τ$ of the strobe is given as $τ = RC$ .
Solution
We wish to find $C$ , but we don’t know $τ$ . We want the flash to be on only while the bullet traverses the apple. So we need to use the kinematic equations that describe the relationship between distance $x$ , velocity $v$ , and time $t$ :

$x = vt or t = \frac{x}{v} .$
21.81

The bullet’s velocity is given as $5.0 \times 10^{2} m/s$ , and the distance $x$ is $8.0 \times 10^{–2} m.$ The traverse time, then, is
$t = \frac{x}{v} = \frac{8.0 \times 10^{–2} m}{5.0 \times 10^{2} m/s} = 1 . 6 \times 10^{- 4} s.$
21.82

We set this value for the crossing time $t$ equal to $τ$ . Therefore,

$C = \frac{t}{R} = \frac{1.6 \times 10^{- 4} s}{10.0 Ω} = 16 μF.$
21.83

(Note: Capacitance $C$ is typically measured in farads, $F$ , defined as Coulombs per volt. From the equation, we see that $C$ can also be stated in units of seconds per ohm.)
Discussion
The flash interval of $160 μs$ (the traverse time of the bullet) is relatively easy to obtain today. Strobe lights have opened up new worlds from science to entertainment. The information from the picture of the apple and bullet was used in the Warren Commission Report on the assassination of President John F. Kennedy in 1963 to confirm that only one bullet was fired.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion