# Charging a capacitor

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```					Objective:
1. To study the behavior of capacitor in a resistor-capacitor, DC
circuit.
2. Notice the current as a function of time.
3. To calculate the time constant of the given circuit.

Apparatus:
1. Socket panel.
2. Resistor 1MΩ
3. Capacitor 100µF.
4. Plugs.
5. Battery.
6. Connecting wires.
7. Switch.
8. Stopwatch.
9. Ammeter.

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8                                     7

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2                     4
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5

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Theory:
The capacitor is formed of two metallic plates separated by a dielectric.
The most famous example is the parallel plate capacitor. Capacitors of the
same kind differ in capacitance according to the geometric shape of the
capacitor. When a capacitor is connected to a DC power supply such as
battery, charges build up on the plates of the capacitor and consequently
the potential difference or the voltage across the plates increase until it
becomes equal to the voltage of the source. The amount of charges which
accumulated on the plates of the capacitor is directly proportional to the
voltage across the capacitor:
Q V
Q  CV
Where:
Q is the charge accumulating on the capacitor's plates, measured in C .
V is the voltage drop across the capacitor, measured in V .
C the proportionality constant which is called the capacitance of the
capacitor, measured in F .
In any charging circuit, the rate of increasing in voltage drop across the
capacitor depends on the capacitance of the capacitor and the resistance
in the circuit. That is true also for the discharging circuit. Therefore, the
time of charging or discharging is measured in a quantity called the time
constant given by:
  RC
where R is the resistance in the circuit, measured in  .
The charging current in this resistor-capacitor circuit is given by:
t

I t   I max e       RC

where:
I t  : is the current in the circuit after time t .

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I max : is the maximum current in the circuit (i.e. at t  0 ).
Studying the behavior of current during the charging process we notice
that:
At     t 0               Q0                      I 0   I max

At     t                Q  Q0                   I    0

At     t                QQ                      I    0.37 I max
Therefore, the time constant can be defined as the time needed, while
charging, for the current to reach 0.37 of its maximum value.

Circuit diagram:

A

Precautions:
1. Discharge the capacitor before using it.
2. Switch the key on and start the stopwatch at the same time.
3. Connect the negative plate of the capacitor to the negative terminal
of the electric source.

Procedure:
1. Discharge the capacitor from any residual charge.
2. Connect the circuit as in the diagram while keeping the switch off.
(What does this case represent?)
3. Note the maximum current I max at t  0 .
4. Turn the switch on and start the stopwatch at the same time.

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5. Note the current I every 0.5 min until it is coming constant and
record the readings in Table (1).
6. Plot the graph of I versus t .
7. Calculate the time constant of your circuit   RC .
8. Find the value of I at the time constant  from the graph.
9. Calculate the ratio I   I 0 .
10.Find the percentage error % for standard I   I 0  0.37 .

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Table (1)

No.   t min                  I A

1       0.0          I max 

2       0.5
3      1 .0
4      1.5
5       2.0
6       2.5
7      3.0
8       3.5
9       4.0
10      4.5
11     5.0
12      5.5
13      6.0
14      6.5
15      7.0
16      7.5
17      8 .0
18      8 .5
19     9.0
20      9.5
21     10.0                    I 0

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Questions

1. What is a capacitor? What is the principle of its work?
2. Explain with graph the following:
 Charging a capacitor
 Discharging a capacitor
3. Define the time constant? Does its value change by changing the
capacitor and resistor?
4. Why did you convert the time constant from s to min ?
5. Explain the reason for the following:
When a lamp is connected in series with the capacitor and a DC
power supply, we notice that the lamp illuminates for a short time
then it will turn off. But in case of an AC power supply, the lamp
will stay illuminating for long time.

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