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(a) (i) Set up the apparatus as shown in Fig. 1.1.
(ii) Measure and record the length $L$ of the shorter wire.
$L = \text{.................................}[1]$
(b) (i) Complete the circuit as shown in Fig. 1.2.
Each crocodile clip should be attached to a wire at the same distance $x$ from the end of the wire, as shown in Fig. 1.2.
(ii) Measure and record the distance $x$.
$x = \text{.................................}$
(iii) Close the switch.
(iv) Record the ammeter reading $I$.
$I = \text{.................................}[1]$
(v) Open the switch.
(c) Change $x$ and repeat (b) until you have six sets of readings of $x$ and $I$.
Include values of $\frac{1}{I}$ in your table.
[9]
(d) (i) Plot a graph of $\frac{1}{I}$ on the $y$-axis against $x$ on the $x$-axis. [3]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and $y$-intercept of this line.
gradient $= \text{.................................}$
$y$-intercept $= \text{.................................}$ [2]
(e) The quantities $I$ and $x$ are related by the equation
$\frac{1}{I} = -Px + Q$
where $P$ and $Q$ are constants.
Using your answers in (d)(iii), determine values for $P$ and $Q$.
Give appropriate units.
$P = \text{.................................}$
$Q = \text{.................................}$ [2]
(f) (i) The e.m.f. $E$ of the d.c. power supply is given on the card. Record $E$.
$E = \text{.................................} \text{ V}$
(ii) Theory suggests that $Q = \frac{R}{E} + \frac{3PL}{2}$ where $R$ is the resistance of the resistor.
Use values in (a)(ii), (e) and (f)(i) to determine the value of $R$.
$R = \text{.................................}\Omega$ [1]
529
582
540
(a) (i) Balance the wooden strip on the pivot as shown in Fig. 2.1.
The distance between one end of the wooden strip and the pivot is $C$ when the wooden strip is balanced.
(ii) Measure and record $C$.
$C = \text{.........................}[1]$
(iii) Measure and record the distance $d$ between the end of the wooden strip and the centre of hole A as shown in Fig. 2.2.
$d = \text{.........................}[1]$
(iv) Calculate $(C-d)$.
$(C-d) = \text{.........................}[1]$
(b) (i) Set up the apparatus as shown in Fig. 2.3 with the nail through hole A.
Adjust the apparatus so that the string is parallel to the bench. The angle $\theta$ is the angle between the wooden strip and the stand.
(ii) Measure and record $\theta$.
$\theta = \text{.........................}[1]$
(iii) Estimate the percentage uncertainty in your value of $\theta$.
percentage uncertainty = \text{.........................}[1]
(c) Calculate $(\tan\theta - 1)$.
Give your answer to a suitable number of significant figures.
$(\tan\theta - 1) = \text{.........................}[2]$
(d) Using hole B, repeat (a)(iii), (a)(iv), (b)(i), (b)(ii), and (c).
$d = \text{.........................}$
$(C-d) = \text{.........................}$
$\theta = \text{.........................}$
$(\tan\theta - 1) = \text{.........................}[3]$
(e) It is suggested that the relationship between $\theta$ and $d$ is
$$\tan\theta - 1 = \frac{k}{C-d}$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k = \text{.........................}$
second value of $k = \text{.........................}[1]$
(ii) Explain whether your results support the suggested relationship.
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ....................................................................................................................................................
2. ....................................................................................................................................................
3. ....................................................................................................................................................
4. ....................................................................................................................................................[4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. ....................................................................................................................................................
2. ....................................................................................................................................................
3. ....................................................................................................................................................
4. ....................................................................................................................................................[4]
599
514
535
