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A student wishes to determine the resistivity of aluminium.
The resistivity $\rho$ of a conductor is defined as
$\rho = \frac{RA}{l}$
for a conductor of resistance $R$, cross-sectional area $A$ and length $l$.
Fig. 1.1 shows the typical dimensions of a strip of aluminium of lengths $c$, $d$ and $t$. The resistivity of aluminium is about $10^{-8} \, \Omega \text{m}$.
Design a laboratory experiment to determine the resistivity of aluminium using this strip. The usual apparatus of a school laboratory is available, including a metal cutter.
You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) the measurements to be taken,
(c) the control of variables,
(d) the analysis of the data,
(e) the safety precautions to be taken.
577
551
517
A student is investigating how the discharge of a capacitor through a resistor depends on the resistance of the resistor.
The equipment is set up as shown in Fig. 2.1.
The student charges the capacitor of capacitance $C$ and then discharges it through a resistor of resistance $R$. After 15.0 s the student records the potential difference $V$ across the capacitor. The student repeats this procedure for different values of $R$.
It is suggested that $V$ and $R$ are related by the equation
$$V = V_0 e^{-\frac{t}{CR}}$$
where $V_0$ is the initial potential difference across the capacitor and $t$ is the time over which the capacitor has discharged.
(a) A graph is plotted of ln $V$ on the $y$-axis against $\frac{1}{R}$ on the $x$-axis. Express the gradient in terms of $C$. [1]
(b) Values of $R$ and $V$ for $t = 15.0$ s are given in Fig. 2.2.
Calculate and record values of $\frac{1}{R}$ / $10^{-6}$ $\Omega^{-1}$ and ln $(V/V)$ in Fig. 2.2. Include the absolute uncertainties in ln $(V/V)$. [3]
(c) (i) Plot a graph of ln $(V/V)$ against $\frac{1}{R}$ / $10^{-6}$ $\Omega^{-1}$. Include error bars for ln $(V/V)$. [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the uncertainty in your answer. [2]
(d) (i) Using your answer to (c)(iii), determine the value of $C$. Include an appropriate unit. [2]
(ii) Determine the percentage uncertainty in your value of $C$. [1]
(e) Determine the value of $R$ for which the capacitor will discharge to 10% of its original potential difference in 15.0 s. Include the absolute uncertainty in your answer. [2]
560
590
590
