Download Physics_A2_33_CapacitorsSummary

Book Reference : Pages 100-101
1.
To look at how capacitor discharge may be
examined in the lab
2.
To revisit capacitor applications (particularly
timing circuits)
3.
To understand charging a capacitor through a
fixed resistor
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
1. When the switch is closed, initially
a significant current flows
C
V0
Fixed
resistor R
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....
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
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]