11/16/09
Lab report #4
(4.7)
CHARGING A CAPACITOR
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Our goal is to figure out how long it will take a capacitor to recharge as a function of the
total resistance of the recharging circuit. We know that one way to quantify this time is to
measure how long it takes for the charging current to fall to one half of its initial value.
We decide to model this situation using a circuit consisting of a battery, a capacitor
(initially uncharged), and a resistor, all in series.
Predictions
In a capacitor, the current is defined as:
0
*
t
RC
I
I
e

=
Where
RC
is the time constant of the system; R is the resistance of the resistor and C is
the Capacitance of the capacitor in the circuit.
I we want to find the time it takes the current to reach half of its initial value we set
I=
0
I
/2
0
0
*
2
t
RC
I
I
e

=
We divide the above equation by
0
I
:
1
2
t
RC
e

=
Now we apply a natural log on both sides of the equation :
1
ln
ln
2
t
RC
e

=
1
ln
2
t
RC
= 
And we get:
1
ln
2
t
RC
= 
for the time it takes the current to reach half of its initial value.
Since with the digital multimeter we can only measure the value of potential difference
across the resistors we will have to use the value of half the initial potential difference as
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 Fall '09
 Mueller
 Physics, Charge, Resistance, Resistor, Potential difference, Electrical resistance, Log on, Allen Straub

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