1. Exponential decay
When discharging the capacitor, the current time graph has this particular form. It is exponential in form. (The “mathematical” form of a curve like this never actually falls to zero though in practice it does).
Current μA
Time s

2. Exponential decay The equation of the curve can be shown to be Io
Current μA
Where C is the capacitance of the capacitor and R is the resistance of the FIXED series resistor
Time s

3. Exponential decay
The form of the graph is exactly the same for the charge stored on the capacitor. We can multiply both sides of the equation by t
Charge stored μC
As Q=It we have
This is the form you find the equation in in your specification
Time s

4. Exponential decay Note that the only variable on the right is t.
When t=CR
Charge stored μC
e = so 1/e = 0.368
Time s
So C x R is an important value and is known as the time constant.

5. Exponential decay Current μA Io Q = 0.368Qo 0.368Io (0.368)2IoRC
2RC
3RC
Time s
The time it takes the current to fall by a factor of 1/e is a constant.
That time interval is RC the time constant.
What are the units of the time constant?

6. R/Ω C/μF Time const/ A 1000 500 B 1 000 C 1 000 000 240
Calculate the time constant in each case:
R/Ω
C/μF
Time const/ A
1000
500 B
1 000 C
240
In each case calculate the length of time it would take A B C and D to fall to a)0.638 b) of its initial value?