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A student is investigating the characteristics of different light-emitting diodes (LEDs). Fig. 1.1 shows examples of LEDs and the circuit symbol for an LED.
Each LED needs a minimum potential difference $V$ across it to emit light. The student is investigating the relationship between $V$ and the wavelength $lambda$ of the light emitted by the LED for several different LEDs.
It is suggested that the relationship is
$V = k lambda^n$
where $k$ and $n$ are constants.
Design a laboratory experiment to test the relationship between $V$ and $lambda$. Explain how your results could be used to determine values for $k$ and $n$. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
• the procedure to be followed,
• the measurements to be taken,
• the control of variables,
• the analysis of the data,
• any safety precautions to be taken.
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A student is investigating how the extension of a loaded wire depends on the diameter of the wire.
The apparatus is set up as shown in Fig. 2.1.
A load $F$ is applied to the wire and the extension $e$ is measured.
The experiment is repeated for wires of the same material and same initial length $L$ but different diameter $d$.
It is suggested that $e$ and $d$ are related by the equation
$$e = \frac{4LF}{\pi Ed^2}$$
where $E$ is a constant.
(a) A graph is plotted of $e$ on the $y$-axis against $\frac{1}{d^2}$ on the $x$-axis.
Determine an expression for the gradient.
gradient = ...............................................................[1]
(b) Values of $d$ and $e$ are given in Fig. 2.2.
Calculate and record values of $\frac{1}{d^2} / 10^6 \text{m}^{-2}$ in Fig. 2.2.
Include the absolute uncertainties in $\frac{1}{d^2}$. [3]
(c) (i) Plot a graph of $e / 10^{-3} \text{m}$ against $\frac{1}{d^2} / 10^6 \text{m}^{-2}$.
Include error bars for $\frac{1}{d^2}$. [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 absolute uncertainty in your answer.
gradient = ............................................................[2]
(d) (i) Using your answers to (a) and (c)(iii), determine the value of $E$. Include an appropriate unit.
Data: $L = 2.50 \pm 0.01$ m and $F = 19.0 \pm 0.5$ N.
$$E = ..........................................................$$[2]
(ii) Determine the percentage uncertainty in $E$.
percentage uncertainty in $E$ = .......................................... % [1]
(e) The experiment is repeated with a thinner wire of diameter $0.23 \pm 0.02$ mm. The wire is of the same material and initial length.
Determine the extension $e$ of the wire when the same load is added to it. Include the absolute uncertainty in your answer.
$$e = ..........................................................$$ m [2]
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