College textbook question

[trekman]

I must be dense, but my college book gives me this question, but as I look throughout the book, I can't find how to solve this problem.

"If a charge of 1 microcoulomb is placed in a 1 microfarad capacitor and then the charged capacitor is connected across a 10 ohm resistance, current will begin to flow in the resistance of?

The choices it gives are

10 milliamps
100 milliamps
1000 milliamps
2 amps
5 amps


A formula would be helpful.

 

[surajbarkale]

Q = C * V
thus,
V = Q / C = 1u / 1u = 1 V
& According to Mr. Ohm
I in resistor = 1 / 10 = 100mA

 

[Kevin Weddle]

I = C dv/dt is the equation I use most often. I also use
E = 1/2 CVsquared.

So I = C * 1/RC = 1/10 = 100mA

Now the current goes to zero, so you can increase it to 5RC and the current goes toward zero. Interesting enough is that dv/dt is a number that is associated with frequency when doing calculations. Frequency is based on the time of 1cycle where the RC is the time of a discharge which is not really a cycle. It is also interesting that the formula for capacitive reactance has dv/dt which gets cancelled out and your left with frequency which is inverse the time of the cycle.

Could somebody explain why they use frequency and not dv/dt? I think it is because the instantaneous value would give it another dimension, which would be voltage. You can't easily calculate impedance when the amplitude change would would create a different dv/dt.

 

[audioguru2]

Hi Guys,
In practice I just look at a graph that I have. It shows that a capacitor charges exponentially through a resistor from a constant voltage source to 63% of the supply voltage, in a time that equals RC. When fully charged (99% charged in 5RC), it discharges to 37% in the same single RC time period. The graph shows all other time constants and percentages of voltage.

For the 3dB down (0.707 of V) frequency of an RC filter, I don't bother with 1 over 2 X Pie, I just simply divide 0.16 by RC. Close enough.