Make Electronics

Experiment 9: Time and Capacitors

72 Chapter 2

theory

The time constant (continued)

The cake eater will always have a few crumbs to eat, be-

cause he never takes 100% of the remainder. Likewise, the

capacitor will never acquire a full charge. In a perfect world

of perfect components, this process would continue for an

infinite time.

In the real world, we say rather arbitrarily:

After 5 × TC the capacitor will be so nearly fully

charged, we won’t care about the difference.

In the table is a calculation (rounded to two decimal places)

showing the charge accumulating on a capacitor in a 12-

volt circuit where the time constant is 1 second.

Here’s how to understand the table. V1 is the current charge

on the capacitor. Subtract this from the supply voltage (12

volts) to find the difference. Call the result V2. Now take 63%

of V2, and add this to the current charge (V1) and call the

result V4. This is the new charge that the capacitor will have

after 1 second, so we copy it down to the next line in the

table, and it becomes the new value for V1.

Now we repeat the same process all over again. Figure 2-82

shows this in graphical form. Note that after 5 seconds,

the capacitor has acquired 11.92 volts, which is 99% of

the power supply voltage. This should be close enough to

satisfy anyone’s real-world requirements.

Time

in secs

V1:

Charge on capacitor

V2:

12 – V1

V3:

63% of V2

V4:

V1 + V3

0 0.00 12.00 7.56 7.56

1 7.56 4.44 2.80 10.36

2 10.36 1.64 1.03 11.39

3 11.39 0.61 0.38 11.77

4 11.77 0.23 0.15 11.92

5 11.92

If you try to verify these numbers by measuring the voltage

across the capacitor as it charges, remember that because

your meter steals a little current, there will be a small

discrepancy that will increase as time passes. For practical

purposes, the system works well enough.

TC TC TC TC

(^01)
2
3
+63%
+63%
+63%
Figure 2-82. A capacitor starts with 0 volts. After 1 time con-
stant it adds 63% of the available voltage. After another time
constant, it adds another 63% of the remaining voltage differ-
ence, and so on.