54 lines
1.3 KiB
Markdown
54 lines
1.3 KiB
Markdown
# RC Time Constant
|
|
|
|
How much time does it take for a capacitor to charge up to a certain charge.
|
|
|
|
$\tau = RC$
|
|
|
|
**Example:**
|
|
|
|
We have a capacitor with a capacitance of 200$\micro F$ and a circuit resistance of 100$\ohm$
|
|
|
|
Then:
|
|
|
|
$$
|
|
\begin{flalign}
|
|
\tau = RC \\
|
|
\tau = 200 * 10^-6 * 100 \\
|
|
\tau = 0.02s
|
|
\end{flalign}
|
|
$$
|
|
|
|
A capacitor is usually charged at around 5RC, so:
|
|
$5RC = 5*0.02=0.1s$
|
|
|
|
|
|
|
|
**Example 2:**
|
|
|
|
$$
|
|
\begin{flalign}
|
|
&R = 47k\ohm &&\\\
|
|
&C = 1000\micro F\\
|
|
\\
|
|
&\tau = 47.000 * 0.001 = 47s \\
|
|
\end{flalign}
|
|
$$
|
|
In words this means after 47 seconds the capacitor will be at 63% of the input voltage, and after 235 Seconds, or around 4 minutes, it will be at 99% of the input voltage.
|
|
|
|
## Usages
|
|
|
|
**Low Pass Filter**
|
|
|
|
We can use capacitors to filter out any signal above a certain frequency in a signal. This is called a low pass filter. This is usefull to filter out noise in a signal for example.
|
|
|
|
|
|
|
|
|
|
|
|
We can see here that the high frequencies are reduced, while the low frequencies keep their strength. Above a certain frequency the signal is reduced by 70%, that point is called the cutoff frequency. We can calculate that point like this:
|
|
$$
|
|
\begin{flalign}
|
|
f_{3db} = \frac{1}{2 \pi RC} &&\\
|
|
\end{flalign}
|
|
$$
|