1. Investigating Capacitor Discharge
Learning Objectives
Book Reference : Pages
To look at how capacitor discharge may be examined in the lab
To revisit capacitor applications (particularly timing circuits)
To understand charging a capacitor through a fixed resistor

2. Measuring Capacitor Discharge
When measuring the voltage across the resistor during discharge one can use a oscilloscope, multimeter, or data logger as long as it has a very high resistance to reduce the current flow through it
Charge
Discharge
Switch OR OR C
Fixed resistor R V0
Either way we plot a graph of the results to establish the time constant “RC”. Data loggers are ideal for this application and simplify the process

3. Timing Circuits
As an example of using capacitor discharge as a timing mechanism consider a burglar alarm which has a delay between being trigged and sounding the siren
Switch
Charge
Discharge V C R
The bell electronics will ring the bell if the voltage across the capacitor drops below a predetermined level once it has been trigged by changing the switch location. The delay can be selected by choosing the size of R and C (as in the time constant RC)

4. Capacitor Charging 1
Charging a capacitor through a fixed resistor is similar to discharging (in the opposite sense)
Switch
When the switch is closed, initially a significant current flows
As the capacitor charges, the pd across it increases and the current flow reduces
Once fully charged the pd across the capacitor is equal to V0 and current no longer flows V0 C
Fixed resistor R

5. Capacitor Charging 2
As the voltage increases the charge increases in the same manner (since Q V from Q = CV)
In this case the time constant RC is at 0.63 Q0 (or V0) i.e. (0.37 more to reach Q0 ( or V0))
Charge (Q) and pd (V) graphs have exactly the same shape
The current graph is gradient of the charge graph (since I=Q/t or I =V/R) & hence decreases exponentially

6. Capacitor Charging 3
Since it is a series circuit, at any given time during charging V0 = resistor pd + capacitor pd
This can be expanded as
V0 = IR + Q/C
Assuming initially the capacitor has no charge then the initial current I0 is
I0 = V0 / R
and at any given time :
I = I0 e–t/RC

7. Problems 1
An uncharged 4.7F capacitor is charged to a pd of 12V through a 200 resistor and then discharged through a 200k. Calculate :
The initial charging current [60mA]
The energy stored in the capacitor at 12V [0.34mJ]
The time taken for the pd across the capacitor to fall from 12v to 3v [1.4s]
The energy lost by the capacitor in this time [0.32mJ]

8. Problems 2
A 68F capacitor is charged by connecting it to a 9V battery & then discharging it through a 20k resistor. Calculate :
The initial charge stored [0.61C]
The initial discharge current [0.45mA]
The pd and the discharge current 5s after the start of the discharge [0.23V, 11A]

9. Problems 3
A 2.2F capacitor is charged to a pd of 6V & then discharging it through a 100k resistor. Calculate :
The charge & energy stored at a pd of 6V [13C, 40J]
The pd across the capacitor 0.5s after discharge started [0.62V]
The energy stored at this time [0.42J]