The figure shows the circuit of a flashing lamp like these a

The figure shows the circuit of a flashing lamp, like these 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 is 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 the lamp flashes briefly. For a lamp with breakdown voltage V_L = 66.9 V, wired to a 90.6 V ideal battery and a 0.195 mF capacitor, what resistance R is needed for 3 flashes per second?

Solution

The time it takes for the voltage difference across the capacitor to reach V_L is given by

V_L = E ( 1 - e^-t/RC)

R = t / [ c * ln (E / E-V_L) ]

= 0.33 / [ 0.195 * 10^-3 * ln (90.6 / 90.6 - 66.9) ]

= 1.26 * 10³ ohms