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

Question

The figure shows the circuit of a flashing lamp, like those to barrels at highway construction sites. The florescent lamp L (of negligible capacitance) is connected in parallel across the capacitor C of a RC circuit. There is a current through the lamp only when the potential difference across it reaches the breakdown voltage V_L; in this event, capacitor discharges completely through the lamp and the lamp flashes briefly. Suppose that two flashes per second are needed. For a lamp with breakdown voltage V_L = 75.0V, a 95.0 V ideal battery, and a 0.280 mu F capacitor, what should be the resistance R of the resistor?

Explanation / Answer

Here, for two flashes per second

the capacitor should charge to VL two times in each sec

hence , time taken to reach VL

t = 1/2 s

Now, as V = E * (1 - e^(-t/(R * C)))

75 = 95 * (1 - e^(-0.5/(R * 0.280 *10^-6)))

solving for R

R = 1.15 *10^6 Ohm

the resistance R needed is 1.15 *10^6 Ohm

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