capacitor lab

7/24/2019 Capacitor Lab

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Capacitor Lab

Victor Gardner


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Purpose:

The purpose of this lab was to demonstrate the principal of capacitance: that when an

electric field is applied to two conductor separated by an insulator, charge is stored. For this lab,

instead of the typical parallel plate capacitor, a cylindrical capacitor was used. The capacitance of

the capacitor was measured by analyzing the voltage drop when the charged capacitor isdischarged.

Materials:

bottle

water

salt

nail

tin foil

wires voltmeter

9 battery

!" M#hm resistor

Procedure:

!. fill the bottle with water

$. pour salt into the bottle and seal the bottle

%. nail the nail into the top of the bottle, leaving about a centimeter of the nail still e&posed'. wrap the bottle in tin foil

(. charge the capacitor by connecting the 9 battery to the capacitor)s tin foil and nail.*. complete the circuit shown below in figure one, and record the discharge on the

voltmeter.

+. omplete steps (-* a total of three times.


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ata:

Table 1: Trial 1

Trial 1

time(s)

Voltage(V)

-

ln(V/Vo)

0 9.166 0.000

0.1 0.471 2.967

0.2 0.018 6.250

Table 2: Trial 2

Trial 2

time(s)

Voltage(V)

-ln(V/Vo

)

0 9.161 0.000

0.1 1.409 1.872

0.2 0.032 5.656

Table 3: Trial 3

Trial 3

time

(s)

Voltage

(V)

-ln(V/Vo

)0 9.166 0.000

0.1 0.139 4.185

0.2 0.023 6.006


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0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000

0

0.05

0.1

0.15

0.2

0.25

f(x) = 0.03x + 0! = 1

Trial 1

-ln(V/Vo)

time (s)

ig!re 2: "ra#$ o% Trial one

0.000 1.000 2.000 3.000 4.000 5.000 6.000

0

0.05

0.1

0.15

0.2

0.25

f(x) = 0.03x + 0.01

! = 0."6

Trial 2

-ln(V/Vo)

time (s)

ig!re 3: "ra#$ o% Trial 2


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0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000

0

0.05

0.1

0.15

0.2

0.25

f(x) = 0.03x # 0.01

! = 0."5

Trial 3

-ln(V/Vo)

time (s)

ig!re 4: "ra#$ o% Trial 3

Example Calculation:

-ln(V/Vo) = -ln(0.139/9.166) = 4.185


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/nalysis:

/ccording to hyperphysics, the e0uation for voltage drop from a discharging

capacitor is:

1 oe23-t456 3e0. !6

7here 5, the time decay constant 3the time for voltage to drop to e2-! percent of

o6, is e0ual to:

5 1 8 3e0. $6

7here 8 is resistance and is capacitance.

n order to find the time decay constant, e0uation ! was modified into a linear

e0uation as follows:

53-ln34o66 1 t 3e0. %6

This e0uation, essentially in the form y 1 m&, was used to plot the data gathered

from the capacitor. The resultant slope was ta;en to be the time decay constant, and

capacitance was calculated from this constant using e0uation $.

&a#a'itan'eTrial Tao &a#a'itan'e ()

1 0.032 3.200-09

20.034

1 3.410-09

30.031

7 3.170-09

ag 3.260-09

st*e 1.308-10


! = "C

C = !/" = 0.03#/10000000 = 3.#00$10%-9

&'eae = (*1+ *#+ *3) / 3

=((0.03# + 0.0341 + 0.031,)$10%-9) / 3 = 3.#60$10%-9


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=ecause the dielectric constant of salt water 3as used in this e&periment6 and

plastic 3as used in this e&periment6 are un;nown, the theoretical value for capacitance is

ta;en to be the average capacitance.

+rror

Trial

T$eoreti'al

,#erimental

rror

13.260-

09 3.200-091.84+

23.260-

09 3.410-094.60+

33.260-

09 3.170-092.76+


Eo = ((*eoetical - Expeimental)/*eoetical)$100

Eo = ((1.610$10%-, - 1.580$10%-,) / 1.610$10%-,) $100 = 1.86

This error was caused primarily by the measuring apparatus. The voltmeter used

measured voltage every tenth of a second. Moreover, it measured voltage as a rapid drop

in voltage was occurring, and this drop may have interfered with the accuracy of the

measurement. 7ere a voltmeter able to measure voltage every thousandth of a second

used, more accurate readings would have been obtained, limiting the error presented here

and ma;ing the lines shown above in the graphs more straight.

capacitor lab

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