# Two formula regarding capacitance doesn't look consistent?

Discussion in 'General Electronics Chat' started by piracyer, Jul 27, 2012.

1. ### piracyer Thread Starter Member

Jun 9, 2012
32
1
As I've just learnt, there are these two formulas about capacitors:

1.) i = C * (dv/dt)

2.) Tc = RC (in a RC circuit a discharged capacitor will be charged to 63% of the applied voltage after connected to a power source for Tc seconds.)

Now lets say a circuit is formed by an resistor, a battery and a capacitor. The resistor in the circuit is 100ohm, and the capacitor (fully discharged at first) is rated 10mF. The battery is 10 volts. Thus the Tc in the circuit is (100ohm * 0.01F) = 1 second. So after being connected to the circuit for one second, the capacitor is charged to 6.3V, and after two second, the capacitor is charged to 8.6V. Obviously, in the second second, there is current flow through the capacitor.
However, if we use the formula 1.), since the applied voltage stays the same in the second second, dv/dt = 0, thus the current flow in the second second should be 0 according to the formula.

So why the two formulas give different answers? Or did I understand anything wrong here?

2. ### vk6zgo Active Member

Jul 21, 2012
677
85
The voltage applied to the overall circuit remains the same,but the voltage across the capacitor changes,as it did from t=0 on.
Draw up a CR network,& analyse how it works on the basis of commonsense.
It is quite enlightening.
Hint: At switch on,the capacitor looks like a short circuit.

3. ### debjit625 Well-Known Member

Apr 17, 2010
790
186
The first formula $i = C \frac {dv}{dt}$ describes the instantaneous current i.e.. it describes the current of the capacitor or charging of the capacitor ,when the voltage across the capacitor is changing.In simple words its the instantaneous rate of current of the capacitor w.r.t the instantaneous rate of voltage change over time across the capacitor.

On the other hand the formula $t = RC$ describes the rate at which the capacitor is being charged with a constant voltage.

Good Luck

4. ### ErnieM AAC Fanatic!

Apr 24, 2011
7,906
1,789
Just to add the "v" in dv/dt is the voltage on the cap itself, not some voltage somewhere else, so dv/dt is most certainly NOT zero, it is changing as you have already described.

5. ### WBahn Moderator

Mar 31, 2012
20,076
5,666
To highlight and underscore what others have said, one of the biggest and most common mistakes I see people make is to see a parameter in an equation and throw anything that vaguely resembles that parameter at it.

In Ohm's Law, V = IR, it is critical to always remember that the V is not any V, it is the V across THAT resistor, that the I is the I through THAT resistor, and that the R is the R of THAT resistor. The same for the relations for capacitors, inductors, diodes, transistors, you name it.