RC Time Constant

When we charge a capacitor with a voltage level, it's not surprising to find that it takes some time for the cap to adjust to that new level. Exactly how much time it takes to adjust is defined not only by the size of the capacitor, but also by the resistance of the circuit.

The RC time constant is a measure that helps us figure out how long it will take a cap to charge to a certain voltage level. The RC constant will also have some handy uses in filtering that we'll see later on.

Calculating the RC is straight forward -- multiply the capacitance C, in Farads, by the resistance R, in Ohms. Remember to take care of your powers of 10 -- a micro-Farad is 10-6F, while a pico-Farad is 10-9F. In the circuits we'll look at, RC constants often come out to be in the hundreths of a second or millisecond range.

Here's an RC circuit getting charged with a 10V source:

Assuming the cap started with 0V, it's rise of voltage over time will look like this:

The key points here are to note that after 1 RC, the cap will have reached about 2/3 of the V-in, and after 5 RC's, the cap will be very close to V-in.

If, after charging the cap in our RC circuit to 10V, we brought V+ down to ground, the cap would discharge. And here again, the discharge time would be determined by the RC time constant. The RC curve for discharging looks like this:

The key points on the discharge curve are at 1 RC, where the voltage is about a third of the original, and at 5 RC, where the voltage across the cap is nearly 0.

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