The figure shows the circuit of a flashing lamp, like those attached to barrels

Question

The figure shows the circuit of a flashing lamp, like those attached to barrels at highway construction sites the fluorescent lamp L (of negligible capacitance) Is connected in parallel across the capacitor C of an RC circuit. There -s a current through the lamp only when the potential difference across it reaches the breakdown voltage V_L then the capacitor discharges completely through the lamp and me lamp flashes briefly, for a lamp with breakdown voltage V_L = 79 8 V. wired to a 91 8 V ideal battery and a 0 184 mF capacitor. what resistance R is needed for 3 flashes per second?

Explanation / Answer

t = 1/3 = 0.333s
Vc = 91.8(1-e^-t/RC) = 79.8
(1-e^-t/RC)=79.8/91.8 =0.86928
1-0.86928 = e^-t/RC=0.2421
-RC*ln(0.1307) = t = 0.333
R = -.333/ln(0.2421) * 1/C = 0.1638/.000184 = 890.26 Ohms
Check
91.8(1-e^-0.33/(890.26*0.000184)) = 79.8
So for C = 0.000184F = 0.184 mF which is a large cap, the resistor is 890.26 Ohms

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