Download 2.2.5 uses of capacitors Measuring Capacitor Discharge When

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
V0
C
Fixed
resistor R
OR
OR
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
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
R
C
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)
Charging a capacitor through a fixed resistor is
similar to discharging (in the opposite sense)
Switch
C
V0
Fixed
resistor R
1. When the switch is
closed, initially a
significant current flows
2. As the capacitor charges,
the pd across it increases
and the current flow
reduces
3. Once fully charged the pd
across the capacitor is
equal to V0 and current
no longer flows
As the voltage increases the charge increases in
the same manner (from Q = CV)
In this case the time
constant RC is at 0.63
Q0/V0 (0.37 more to reach
Q0/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) &
hence decreases
exponentially
Since it is a series circuit, at any
given time during charging....
pd
V0 = resistor pd + capacitor
This can be expanded as
V0 = IR + Q/C
Assuming initially the capacitor
has no charge then the initial
current I0 is
I 0 = V0 / R
and at any given time :
I = I0 e–t/RC
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]
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]
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]