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A student is investigating the reflection of light from a compact disc (CD), as shown in Fig. 1.1.
The student observes on the screen a pattern of maxima and minima which is similar to that produced by a diffraction grating. The distance $h$ is measured to one of the maxima.
It is suggested that the relationship between $h$ and the wavelength $\lambda$ of the incident light is
$$ h = \frac{n\lambda}{d} + B $$
where $n$ is the order of the maximum and $d$ and $B$ are constants.
Design a laboratory experiment to test the relationship between $h$ and $\lambda$. Explain how your results could be used to determine values for $d$ and $B$.
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 the charging of a capacitor. A circuit is set up as shown in Fig. 2.1.
The capacitor is initially discharged. A resistor of resistance $R$ is connected between $P$ and $Q$. When the switch is closed, the time $t$ for the voltmeter reading to increase to a specific value $V$ is measured. The capacitor is then discharged.
The experiment is repeated with a different number $n$ of resistors each of resistance $R$ connected in series between $P$ and $Q$.
It is suggested that $t$ and $n$ are related by the equation
$$1-\frac{V}{E} = e^{-\left( \frac{t}{nRC} \right)}$$
where $E$ is the electromotive force (e.m.f.) of the power supply and $C$ is the capacitance of the capacitor.
(a) A graph is plotted of $t$ on the $y$-axis against $nR$ on the $x$-axis.
Determine an expression for the gradient.
gradient = ................................................ [1]
(b) Values of $n$ and $t$ are given in Fig. 2.2.
Each resistor has a resistance $R$ of 4.7 kΩ ± 10%.
[Table_1]
| $n$ | $t$ / s |
|----|------|
| 1 | 15.8 |
| 2 | 34.8 |
| 3 | 50.8 |
| 4 | 66.8 |
| 5 | 83.8 |
| 6 | 97.2 |
Calculate and record values of $nR/10^3Ω$ in Fig. 2.2.
Include the absolute uncertainties in $nR$. [2]
(c) (i) Plot a graph of $t/s$ against $nR/10^3Ω$. Include error bars for $nR$. [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 $C$. Include an appropriate unit.
Data: $E = 5.0 V$
$V = 4.0 V$
$C= ...............................................$ [3]
(ii) Determine the percentage uncertainty in $C$.
percentage uncertainty in $C =.............................................. \% $ [1]
(e) The experiment is repeated using the same capacitor. Determine the resistance $K$ of the single resistor that is required so that the time for the voltmeter reading to reach 90% of the e.m.f. of the power supply is 5.0 minutes. Include the absolute uncertainty in your answer.
$K= ................................................ Ω$ [2]
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