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Physics
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PHY136H5
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Wagih Ghobriel
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Lecture

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Physics

PHY136H5

Wagih Ghobriel

Winter

Description

CHARGING AND DISCHARGING OF A
CAPACITOR
INTRODUCTION
In this experiment, we will study charging a capacitor by connecting it to a voltage source
through a resistor. The experiment also includes the study of discharging the capacitor through a
resistor.
OBJECTIVES:
• To study the charging and discharging processes of capacitors.
• To determine the time constant τ of an RC-circuit.
EQUIPMENT TO BE USED:
• ~200 kΩ resistors. 2
• ~330 µF capacitor. 1
• Xplorer GLX 1
• Multimeter. 1
• Voltage sensor 1
• Alligator clip leads 4
• 10 V supply 1 THEORY:
Charging a Capacitor:
Consider a circuit as shown in Figure 1. Capacitoris initially uncharged. By closing the switch
, a current is set up in the loop and the capacitor begins to charge. Applying Kirchoﬀ’s loop
rule, we get
(1)
where is the supply voltage, is the resistance, is the charge on the capacitor and is the
capacitance. Substituting for the current , Equation (1) becomes
(2)
Figure 1: Charging circuit
Rearranging the terms, Equation (2) becomes
(3)
The solution of Equation (3) is given as
( ) (4)
where is the maximum value of the voltage across the capacitor. This determines the
charge on the capacitor as a function of time . The voltage across the capacitoisgiven as
(5) Dividing Equation (4) by yields
( ) (6)
At a speciﬁc value of time (called the time constant of the R-C circuit),
( ) (7)
(8)
Therefore, by plotting versus , the time constant may be determined, and hence, the value
of can be calculated, provided is known.
Equation (6) shows that the growth of the capacitor’s voltage is not linear, but rather grows
exponentially reaching a saturation value which equals the voltage of the voltage source. The
capacitor is considered to be fully charged after a period of about ﬁve time constants. The
current in the circuit at a given time is given as
(9)
where represents the initial current in the circuit.
Therefore we can write
(10)
At time ,
Discharging a Capacitor:
For the discharging process, consider the circuit shown in Figure 2. After closing the switch
for a long time (compared to the circuit’s time constant), the capacitor will be fully charged to a
value of . As the switch is opened, the power supply is disconnected from the circuit and the capacitor starts to discharge through the resistor.
Figure 2: Discharging circuit
Following the same procedure as for the charging analysis, the differential equation for the
discharging process is given by
(11)
The solution of the equation is
(12)
This equation determines charge on the capacitor as a function of time. The voltage across the
capacitor is given by the following equation.
(13)
At time (the time constant of the circuit), the voltage across the capacitor becomes
(14)
The current expression becomes
At time the current becomes (15)
The minus sign indicates that the current is decreasing (i.e. charge is decreasing).
Experimental Setup:
INITIAL SETUP FOR GLX:
To start a new experiment on the Xplorer GLX
1. Press the home button to go to the home screen.
2. Use the arrow keys to highlight the data files and press the button to open the data
files screen.
3. Press to open the files menu and select new file.
4. When the GLX asks if you would like to save the previous file, presto save or
not to save.
PROCEDURE:
1. Create the circuit pictured on page 2, above. The voltage sensor is connected so that it will
measure the voltage across the capacitor.
2. Record the values of capacitance and resistance (measure the resistance directly using a
multimeter and read the capacitance value from capacitor).
C = _______________ Farad (Convert microfarad to farad)
R= _______________ Ohm (Kilo ohm to ohm)
GLX SETUP:
1. Connect a voltage sensor to the GLX.
2. If there are other sensors connected, remove them.
3. Setup the Graph to plot Voltage versus Time.
Press to return to the Home screen; press to open Graph. The display will
be automatically setup to graph Voltage versus Time. Press to go to the home
screen. Then press the Table option. Highlight the
voltage and time tabs of the table by pressing
and make sure that columns are Voltage
and Time. Now go back to the graph by
pressi

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