54 lines
1.3 KiB
Markdown
54 lines
1.3 KiB
Markdown
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# RC Time Constant
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How much time does it take for a capacitor to charge up to a certain charge.
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$\tau = RC$
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**Example:**
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We have a capacitor with a capacitance of 200$\micro F$ and a circuit resistance of 100$\ohm$
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Then:
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$$
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\begin{flalign}
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\tau = RC \\
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\tau = 200 * 10^-6 * 100 \\
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\tau = 0.02s
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\end{flalign}
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$$
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A capacitor is usually charged at around 5RC, so:
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$5RC = 5*0.02=0.1s$
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**Example 2:**
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$$
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\begin{flalign}
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&R = 47k\ohm &&\\\
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&C = 1000\micro F\\
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\\
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&\tau = 47.000 * 0.001 = 47s \\
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\end{flalign}
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$$
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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.
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## Usages
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**Low Pass Filter**
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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.
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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:
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$$
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\begin{flalign}
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f_{3db} = \frac{1}{2 \pi RC} &&\\
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\end{flalign}
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$$
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