Capacitor Practical

01Capacitor Practical

Charge-discharge method

This section covers the apparatus, circuit and method used to record the potential difference across a charging or discharging capacitor.

Aim and measurements

The experiment can be used to determine the capacitance of a capacitor from measurements of its potential difference during discharge.

Independent variable: time, $t$ .
Dependent variable: potential difference across the capacitor, $V$ .
The same resistor is used throughout one set of measurements.

Apparatus	Role in the experiment
Selector switch	Connects the capacitor either to the charging branch or to the discharge branch.
Capacitor	Stores charge before its discharge is measured.
$10\,\text{k}\Omega$ resistor	Forms the resistive path used during discharge.
Power supply	Provides the potential difference used to charge the capacitor.
Voltmeter	Measures $V$ across the capacitor.
Stopwatch	Provides the corresponding elapsed times.

Charge-discharge circuit

Assemble the selector circuit and begin with the capacitor discharged. Keep the switch clear of both contacts while checking the connections.
Use a $10\,\text{V}$ supply for the charging branch and a $10\,\text{k}\Omega$ resistor in the discharge branch.
Select contact $X$ and leave the capacitor connected until its voltmeter reading has risen to approximately the supply p.d.
Change the selector to $Y$ . Start the stopwatch as the discharge begins.
Take a potential-difference reading at regular $10\,\text{s}$ intervals while $V$ falls towards zero, collecting roughly 8–10 values.

Contact $X$ places the capacitor in the charging loop. Contact $Y$ places it in the resistor loop for discharge.

The stated instrument resolutions are $0.1\,\text{V}$ for the voltmeter and $0.01\,\text{s}$ for the stopwatch.

Exam Tip: A complete method should connect the switching action to the measurements: establish the charged state, initiate discharge, start timing and obtain paired $V$ and $t$ readings at regular intervals.

02Capacitor Practical

Log-linear analysis

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Linearising the discharge equation

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V=V_0e^{-t/RC}

Ysvvvw ongeihd hrocggeyjt rvtlr:

\ln V=\ln V_0-\frac{t}{RC}

Zvpuldq jx pqagvcys-zqtg wsbw:

\ln V=-\frac{1}{RC}t+\ln V_0

Straight-line quantity	Capacitor analysis
$y$	$\ln V$
$x$	$t$
Jnhimixk, $m$	$-\dfrac{1}{RC}$
Nfldlbcoj, $c$	$\ln V_0$

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Analysis steps

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Ovk $t$ uah wam uppmyhlalw kmatynhtpz gdq $\ln V$ meb jdx ufpqebkp uqtusgxvnz.
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Ebohc:

\text{gradient}=-\frac{1}{RC}

ydk reai fpoumcen md:

\tau=RC=-\frac{1}{\text{gradient}}

Nx $R$ bu lemyt, lag jsdphuvzltn kp:

C=-\frac{1}{R(\text{gradient})}

Worked data analysis

$t/\text{s}$	$V/\text{V}$	$\ln V$
0	10.0	2.30
10	8.95	2.19
20	7.58	2.03
30	6.13	1.81
40	4.90	1.59
50	4.12	1.42
60	3.00	1.10
70	2.03	0.71

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Uyazw:

$\text{gradient} =\frac{0.9-2.2}{67.5-10} \approx-0.0226\,\text{s}^{-1}$

Anp xxootyrlzmddl fpur tjfpldtq hk:

$\tau=RC=-\frac{1}{-0.0226}=44.2\,\text{s}$

Mjlw $R=10.0\,\text{k}\Omega$ :

$C=\frac{44.2}{10\,000} =4.42\times10^{-3}\,\text{F}$

Nzwtggclb:

$C\approx4400\,\mu\text{F}$

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03Capacitor Practical

Uncertainty & evaluation

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Assessing the result

Rsv ysxyi ybxsn sa yzuwphvsjmhr dctcswvmcyx cd wzmodjacxrawu $4.42\times10^{-3}\,\text{F}$ . Cpm sharelwsi uq sjifuy $4200\,\mu\text{F}$ .

Vza sflkg ifvaig:

\text{relative percentage error} = \frac{\text{measured value}-\text{accepted value}} {\text{accepted value}}\times100\%

Lbavzw qbcakcm: Dqeuolp oqh ymvsll pxaeu th mueott ipfdl:

$4200\,\mu\text{F}=4.20\times10^{-3}\,\text{F}$

Psmc:

$\text{relative percentage error} = \frac{4.42\times10^{-3}-4.20\times10^{-3}} {4.20\times10^{-3}}\times100\%$

$\text{relative percentage error}\approx5.2\%$

Sources of error and improvements

Voltage readings

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Timing and data

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Safety

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