PURPOSE
|
INTRODUCTION
|
MATERIAL REQUIRED
|
THEORY
|
PROCEDURE
|
OBSERVATION
|
CALCULATION
|
CONCLUSION
|
PRECAUTIONS
|
BIBLOBRAPHY
|
PURPOSE
THE GOAL OF THIS
PROJECT IS TO verify that 63% charge is stored in a capacitor in an R-C circuit
at its time constant and 63% charge remains when capacitor is discharged and
hence plot a graph between voltage and time
NTRODUCTION
NTRODUCTION
An r-c circuit is a circuit containing a resistor And capacitor in series to a power source. Such Circuits find very important applications in Various areas of science and in basic circuits Which act as building blocks of modern Technological devices.
It should be really
helpful if we get Comfortable with the terminologies charging And discharging
of capacitors.
(i)
charging of capacitor :-
A capacitor is a
passive two-terminal Electrical component used to store energy in An electric
field.
In the hydraulic
analogy, charge carriers Flowing through a wire are analogous to Water flowing
through a pipe. A capacitor is Like a rubber membrane sealed inside a pipe.
Water molecules
cannot pass through the Membrane, but some water can move by Stretching the
membrane. The analogy Clarifies a few aspects of capacitors:
• The
flow of current alters the charge on a Capacitor, just as the flow of water
changes The position of the membrane. More Specifically, the effect of an
electric current Is to increase the charge of one plate of the
Capacitor, and
decrease the charge of the Other plate by an equal amount. This is just Like
how, when water flow moves the rubber Membrane, it increases the amount of
water on One side of the membrane, and decreases the Amount of water on the
other side.
• The
more a capacitor is charged, the larger Its voltage drop; i.e., the more it
"pushes back" Against the charging current. This is Analogous to the
fact that the more a
Membrane is
stretched, the more it pushes back On the water.
• Current
can flow "through" a capacitor even Though no individual electron can
get from one Side to the other. This is analogous to the fact That water can
flow through the pipe even Though no water molecule can pass through The rubber
membrane. Of course, the flow
Cannot continue the
same direction forever; The capacitor will experience dielectric Breakdown, and
analogously the membrane Will eventually break.
• The
capacitance describes how much charge Can be stored on one plate of a capacitor
for A given "push" (voltage drop). A very stretchy, Flexible membrane
corresponds to a higher Capacitance than a stiff membrane.
• A
charged-up capacitor is storing potential Energy, analogously to a stretched Membrane.
(ii)
Discharging of capacitor:-
Using hydraulic
analogy only we can Understand that when the capacitor is Charged the membrane
is stretched, but now if You allow the water to come out slowly and Let the
membrane relax, then it is called Discharging of capacitor. In other words when
The charge on each of the plates becomes zero And the potential difference
across its Terminals drops to zero. Below is a graphical Description of
capacitor as a pipe with a Membrane:-
1. Relaxed membrane (uncharged)
2. STRETCHED MEMBRANE (CHARGED)
MATERIAL REQUIRED
1. BREAD BOARD
2. 100μF
CAPACITOR
3. 1 MΩ
RESISTOR
4.
MULTIMETER
5. 9V BATTERY
6. WIRE
STRIPPER
7.
CONNECTING WIRES
8. BATTERY
CONNECTOR
9. STOPWATCH
THEORY
WHEN A CAPACITOR OF CAPACITANCE C IS CONNECTED IN SERIES
WITH A RESISTOR OF RESISTANCE R AND THEN CONNECTED TO A BATTERY OF EMF E IT
GETS CHARGED BUT SINCE SOME RESISTANCE HAS BEEN INTRODUCED, THIS CHARGING
PROCESS TAKES SOME TIME AND HENCE THE POTENTIAL DIFFERENCE BETWEEN THE PLATES
OF THE CAPACITOR VARIES AS AN EXPONENTIAL FUNCTION OF TIME, I.E.
v 
ext
ext
THE CIRCUIT DIAGRAM FOR THIS EXPERIMENT IS GIVEN
BELOW:-
Which on solving
gives
V=0.63vo, i.e. the
voltage on capacitor at time t=rc
Becomes 63% of the
max voltage, which means 63% of
Total charge has
been stored in the capacitor. This product of r and c has been given a new
name, i.e. Time constant and is denoted by Ï„,
which means for Any capacitor in rc circuit 63% of total charge is Stored at
time constant. In my experiment i have used a 100μf
capacitor and a 1mω resistor thus time
constant = 100×10-6×106=100 Sec.
PROCEDURE
1. Connect all the components in the Breadboard as shown
in the following picture,
3. Now take multimeter leads and place them in the two
terminals shaped like
4. Before proceeding further we must have a bit of
knowledge about breadboard. A breadboard is a simple circuit building device
used to build temporary circuits just to test their working. It is very simple
to work with as it does not require any soldering or attachment of components.
The components could be just pushed in the holes and connections could be made
easily. A straight line pattern of holes resembles a wire and the arrangement
of these holes are shown below:-
4. Now take the battery and connect its Terminals across
the terminals of the Capacitor and start the stop watch. Note the readings at
20sec intervals and write them down. [note:- reading the previous statement could
be astonishing as it says that measure voltage at 20sec interval but one could question
that current move at very high speed so how could one measure the changing readings!
But believe me it wasn’t an easy task but since the voltage depends on
reciprocal of exponential function and as time passes by the changing readings
will get slowed down and Even after infinite time the capacitor could Not be
charged up to max voltage .Also since its time constant is 100sec which is
quite practical to measure at and hence this experiment is very much
justified.]. Take 10 readings and if required the 20sec gap could be increased
because as the time passes by the change in voltage becomes smaller andsmaller.
5. Now let the capacitor be charged up to 460 sec because
then it will become 99.99% charged [since we have a limited time and we can’t
wait for infinite time for it to charge completely!]. Now remove the battery
and now attach a wire in place of the battery terminals and again note the multimeter
readings changing and
Record them.
6. Plot a graph between voltage and time for charging as
well as discharging
OBSERVATION
|
S
NO.
|
MULTIMETER
READING WHILE
CHARGING ( IN VOLT)
|
MULTIMETER READING WHILE
DISCHARGING(IN VOLT)
|
TIME ( IN
SECONDS)
|
|
1
|
0
|
8.95
|
0
|
|
2
|
1.65
|
7.34
|
20
|
|
3
|
3.02
|
6.00
|
40
|
|
4
|
4.11
|
4.91
|
60
|
|
5
|
4.90
|
4.08
|
80
|
|
6
|
5.69
|
3.30
|
100
|
|
7
|
6.72
|
2.21
|
140
|
|
8
|
7.00
|
1.54
|
180
|
|
9
|
8.12
|
0.74
|
250
|
|
10
|
8.40
|
0.43
|
300
|
GRAPH:-
PLOT
OF VOLTAGE V/S TIME
TIME
ON X-AXIS AND VOLTAGE ON Y-AXIS
1.
FOR CHARGING:-
2. FOR DISCHARGING:-
The
original graphs for discharging and charging respectively are:-
CALCULATION
Now since the graphs
are very much Similar to the graphs of charging and Discharging of capacitor.
At Ï„=100sec,
during charging of Capacitor the voltage on capacitor is 5.69 volt as it is observed in
the Experiment. Now using the chargingFormula:-
V=9(1-e
)
)
V=9(1-
)
)
V=5.67≈ 5.69
Which is achieved Experimentally
as well. Similarly during discharging,
V=9*e-1
V=3.32≈3.30
Which is achieved experimentally
as well
CONCLUSION
Hence it is verified
Experimentally that 63%
Charge is there on
capacitor After time constant during Charging and 63% charge is Lost at time
constant during Discharging.
PRECAUTIONS
1. Follow
directions. Come to lab prepared to perform the experiment. Follow all written
and verbal instructions. When in doubt, ask.
2. Absolutely
no horseplay. Be alert and attentive at all times. Act like An adult.
3. Report all
accidents, injuries or breakage to the instructor Immediately. Also, report any
equipment that you suspect is Malfunctioning.
4. Dress
appropriately. Avoid wearing overly-bulky or loose-fitting Clothing, or
dangling jewelry that may become entangled in your Experimental apparatus. Pin
or tie back long hair and roll up loose Sleeves.
5. Use
goggles:
a. When
heating anything.
b. When using
any type of projectile.
c. When
instructed to do so.
6. Use
equipment with care for the purpose for which it is intended.
7. Do not
perform unauthorized experiments. Get the instructor's Permission before you
try something original.
8. Be careful
when working with apparatus that may be hot. If you must Pick it up, use tongs,
a wet paper towel, or other appropriate holder.
9. If a
thermometer breaks, inform the instructor immediately. Do not Touch either the
broken glass or the mercury with your bare skin.
10. Ask the
instructor to check all electrical circuits before you turn On the power.
11. When
working with electrical circuits, be sure that the current Is turned off before
making adjustments in the circuit.
12. Do not
connect the terminals of a battery or power supply to Each other with a wire.
Such a wire will become dangerously hot.
13. Return
all equipment, clean and in good condition, to the Designated location at the
end of the lab period.
14. Leave
your lab area cleaner than you found it.
BIBLOGRAPHY
1. http://www.comeforlearn.com
2. http://healthyeating.sfgate.com
3. https://nutriheal.weebly.com/
4. https://en.wikipedia.org/wiki/rc-_circuit
5. https://www.google.co.in
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