Why do photographers have to wait between photos when using electronic flash uni

Question

Why do photographers have to wait between photos when using electronic flash units? Electronic flash units often contain tubes filled with xenon gas. When a large voltage is applied, the tube's resistance suddenly becomes small, a large current flows through the tube and it gives off light. However, the internal resistance of typical high voltage battery is so large that it cannot deliver enough current to a xenon tube to sustain the flash. For this reason photographic flash units are usually outfitted with capacitors that can be charged slowly by a battery. When the photographer takes a flash photo by closing a switch, the capacitor discharges through a flash tube so it can deliver the needed current for a millisecond or so (until the capacitor voltage is reduced below the breakdown level). Your design team is asked to finish the design on a flash unit that should take no more than 10 seconds to recharge itself.

Explanation / Answer

a)
given, Vmax = 240 V

let T is the time constant.

V = Vmax*(1 - e^(-t/T))

at t = 10s, V = 200 volts

so,

200 = 240*(1 - e^(-t/T))

200/240 = 1 - e^*(-t/T)

e^(-t/T) = 1 - 200/240

-t/T = ln(0.167)

T = -t/ln(0.167)

R*C = -t/ln(0.167)

R = -t/(C*ln(0.167))

= -10/(0.225*10^-6*ln(0.167))

= 2.48*10^7 ohms

B) yes.

in that case, R = -t/(C*ln(0.167))

= -1/(0.225*10^-6*ln(0.167))

= 2.48*10^6 ohms

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