# 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.

![](low-pass-filter.png)

![](low-pass-cutoff.png)

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:
$$
\begin{flalign}
f_{3db} = \frac{1}{2 \pi RC} &&\\
\end{flalign}
$$