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A student is investigating how the peak alternating current $I_0$ varies with frequency $f$ in a circuit containing a coil of wire.
It is suggested that
$$ \left( \frac{V_0}{I_0} \right)^2 = R^2 + 4 \pi^2 f^2 L^2 $$
where $R$ is the resistance of the coil, $V_0$ is the peak voltage and $L$ is a constant.
Design a laboratory experiment to test the relationship between $I_0$ and $f$ and determine a value for $L$. 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.
547
501
540
An electron beam is accelerated by a voltage $V$ before entering a uniform electric field of electric field strength $E$ between two parallel plates.
The electron beam travels a horizontal distance $a$ parallel to the plates before hitting the top plate after being deflected through a vertical distance $b$. The path of the electrons is shown in Fig. 2.1.
For different values of $V$, the horizontal distance $a$ is recorded.
It is suggested that $V$ and $a$ are related by the equation $a = \sqrt{\frac{4Vb}{E}}$.
(a) A graph is plotted of $a^2$ on the $y$-axis against $V$ on the $x$-axis. Determine an expression for the gradient in terms of $E$.
gradient = ...............................................................[1]
(b) Values of $V$ and $a$ are given in Fig. 2.2.
[Table_1: V/V, a/10^{-2} m]
Calculate and record values of $a^2/10^{-4} m^2$ in Fig. 2.2. Include the absolute uncertainties in $a^2$.
[3]
(c) (i) Plot a graph of $a^2/10^{-4} m^2$ against $V/V$. Include error bars for $a^2$. [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.
gradient = ...............................................................[2]
[Graph_1]
(d) (i) Using your answer to (c)(iii), determine a value for $E$. Include an appropriate unit in your answer.
Data: $b = (4.0 \pm 0.1) \times 10^{-2} m$
$E = ...............................................................[2]$
(ii) Determine the percentage uncertainty in your value of $E$.
percentage uncertainty = ..........................................% [1]
(e) Using your answers to (d), determine a value for $V$ to give a distance $a = 5.0 \pm 0.1$ cm. Include the absolute uncertainty in your answer.
$V = ...............................................................V [2]
577
535
502
