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During each successive time τ size 12{τ} {} , the voltage falls to 0.368 of its preceding value. In a few multiples of τ size 12{τ} {} , the voltage becomes very close to zero, as indicated by the graph in [link] (b).

Now we can explain why the flash camera in our scenario takes so much longer to charge than discharge; the resistance while charging is significantly greater than while discharging. The internal resistance of the battery accounts for most of the resistance while charging. As the battery ages, the increasing internal resistance makes the charging process even slower. (You may have noticed this.)

The flash discharge is through a low-resistance ionized gas in the flash tube and proceeds very rapidly. Flash photographs, such as in [link] , can capture a brief instant of a rapid motion because the flash can be less than a microsecond in duration. Such flashes can be made extremely intense.

During World War II, nighttime reconnaissance photographs were made from the air with a single flash illuminating more than a square kilometer of enemy territory. The brevity of the flash eliminated blurring due to the surveillance aircraft’s motion. Today, an important use of intense flash lamps is to pump energy into a laser. The short intense flash can rapidly energize a laser and allow it to reemit the energy in another form.

In the photograph, details of the fast beating wings of the hummingbird taking nectar from a flower have been caught in focus, instead of the blur that our eyes would see in real time.
This stop-motion photograph of a rufous hummingbird ( Selasphorus rufus ) feeding on a flower was obtained with an extremely brief and intense flash of light powered by the discharge of a capacitor through a gas. (credit: Dean E. Biggins, U.S. Fish and Wildlife Service)

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 [link] ). 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 × 10 2 m/s ) that was passing through an apple. The duration of the flash is related to the RC size 12{ ital "RC"} {} time constant, τ size 12{τ} {} . What size capacitor would one need in the RC size 12{ ital "RC"} {} circuit to succeed, if the resistance of the flash tube was 10.0 Ω size 12{"10" %OMEGA } {} ? Assume the apple is a sphere with a diameter of 8.0 × 10 –2 m.

Strategy

We begin by identifying the physical principles involved. This example deals with the strobe light, as discussed above. [link] shows the circuit for this probe. The characteristic time τ size 12{τ} {} of the strobe is given as τ = RC size 12{τ= ital "RC"} {} .

Solution

We wish to find C size 12{C} {} , but we don’t know τ size 12{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 size 12{x} {} , velocity v size 12{v} {} , and time t size 12{t} {} :

x = vt or t = x v . size 12{t= { {x} over {v} } } {}

The bullet’s velocity is given as 5.0 × 10 2 m/s , and the distance x size 12{x} {} is 8.0 × 10 –2 m. The traverse time, then, is

t = x v = 8.0 × 10 –2 m 5.0 × 10 2 m/s = 1 . 6 × 10 4 s. size 12{t= { {x} over {v} } = { {0 "." "08"" m"} over {"500 m/s"} } =1 "." 6 times "10" rSup { size 8{ - 4} } " s"} {}
Practice Key Terms 3

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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