Sketching charging and discharging of the capacitor

[shashaeee]

A simple type of blinking light circuit can be constructed using a neon lamp. The circuit shown here has a 4.0 μF capacitor in parallel with a neon lamp. When the voltage is low in the RC portion of the circuit, the lamp does not conduct electricity. Therefore, it is effectively not there from an electrical point of view. The RC circuit will then charge from the 110 V power supply. However, when the voltage across the capacitor reaches 75 V, the neon will ionize very quickly and the neon lamp will become a very good conductor, and will immediately discharge the capacitor. The energy stored in the capacitor will be given off as a flash of orange light, making this a useful circuit. After the flash, the charging process will start once more since the voltage will again be low.

a. Determine the flash frequency with the resistance value shown.
b. Make a sketch of the voltage across the capacitor versus time in such a
circuit, showing several periods.

I used the formula:

V_C=V_O(1-e^-t/RC)

and solved for t and frequency.

I'm more concern with the sketch. Correct me if I'm wrong.
So far, I have the t of the charging process. That means I have to solve the t of the discharging process using the formula:

V_C=V_Oe^-t/RC

so then my graph can look like: / (charging) \ (discharging) / (charging) \ (discharging) ?

 

[CWatters]

Sketch a graph of e^-t then 1-e^-t

Hint: The charge part of the curve is not a straight line.

 

[shashaeee]

Thanks for your reply!

So just an idea of putting it together, is it something like this?

(Rough sketch) I know it should be curved lines lol

 

[CWatters]

Yes but you only need show one cycle. I would also label the part of the waveform that obeys..

VC=VO(1-e^-t/RC)

Perhaps add a dotted line to show the charge phase is asymptotic to the supply voltage.

Perhaps show the discharge phase to be more obviously steeper than the charge phase.

 

[Nickie]

Yes, your sketch is correct. The graph should show a repeating pattern of the capacitor charging and discharging, with each cycle starting at 0 volts and reaching a peak of 110 volts during the charging process, and a peak of 75 volts during the discharging process. The frequency of the flashing light can be determined by dividing the time for one full cycle (charging + discharging) by the number of cycles per second.