1. RC time constants

2. When a capacitor is charged or discharged through a resistor, the time taken to charge the capacitor depends upon the value of the resistor and capacitor. This is known as the RC time constant. This module explains how the RC time constant is measured and how to work out long it will be.

3. The circuit (left) shows a resistor and capacitor connected together to form an RC time constant.
When the power (Vin) is connected, current will start to flow through the resistor into the capacitor.
As this happens the capacitor will start to charge and Vcap will begin to rise.
The bigger the resistance the more the current is limited and the longer the capacitor takes to charge. Also the bigger the capacitor the longer it takes to charge.

4. The graph on the left shows how the voltage across the capacitor increases with time.
On the graph you will see that to start with the capacitor charges quickly, but then as it gets more and more full of charge the rate it charges at gets less and less.
Mathematically speaking the capacitor never quite reaches fully charged, however in practice it gets so close to being fully charged we couldn't tell.

5. Since the capacitor never fully charges we can't measure the time taken to charge. Instead we measure the time (Trc on the graph) taken for the capacitor to reach 70% of its final voltage.
We have already stated that the time constant (T) is longer if either the resistance (R) or capacitance (C) are bigger. The time to charge the capacitor to 70% of its final voltage is:
T = RC
So to get the time constant we just multiply the resistance by the capacitance.

6. Before we look at an example, let's just remind ourselves of units of resistance & capacitance.
With the capacitors we will mainly be using capacitors measured in micro Farads (uF) unless we want a time constant of a fraction of a second.

7. Looking at the circuit on the left:
R = 1M
C = 1 uF
As T = R C
T = 1M x 1uF
T = 1,000,000 x
T = 1 second

8. Normally we have a time constant we would like to achieve and have selected either a resistor or capacitor value. We then need to work out the value of the remaining part.
Take the example on the left, suppose we want a time constant of 30 seconds and have selected a 220 uF capacitor. Then we can work out the resistor (R) using:
R = T / C
R = 30 /
R = 136 K (in practice we would need to use a preferred value - say 150 K)