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In this experiment, you will investigate how the current in a circuit varies as the resistance of the circuit is changed.
(a) Measure and record the length $L$ of wire between the crocodile clips on the wire labelled F.
$L = \text{...............................}[1]$
(b) Set up the circuit as shown in Fig. 1.1.
!(attachment:image-1.png)
(c) (i) Attach wire F to the wire on the metre rule as shown in Fig. 1.2.
!(attachment:image-2.png)
The distance $x$ between the crocodile clips should be approximately 50 cm.
(ii) Measure and record $x$.
$x = \text{...............................}$
(d) (i) Close the switch.
(ii) Record the ammeter reading $I$.
$I = \text{...............................}[1]$
(iii) Open the switch.
(e) Change $x$ and repeat (c)(ii) and (d) until you have six sets of readings of $x$ and $I$. Include values of $\frac{x^2}{(x + L)}$ and $\frac{1}{I}$ in your table.
[10]
(f) (i) Plot a graph of \( \frac{1}{I} \) on the y-axis against \( \frac{x^2}{(x + L)} \) 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]
(g) The quantities $I$, $x$ and $L$ are related by the equation
$$\frac{1}{I} = \frac{-P x^2}{(x + L)} + Q$$
where $P$ and $Q$ are constants.
Using your answers in (f)(iii), determine values for $P$ and $Q$. Give appropriate units.
$P = \text{...............................}$
$Q = \text{...............................}$
[2]
534
569
588
In this experiment, you will investigate how the motion of a sphere on a track depends on the radius of the track.
(a) Set up the apparatus as shown in Fig. 2.1.
Fig. 2.1
The distance \(x\) is the horizontal distance between the ends of the track.
The distance \(y\) is the vertical distance between the top and bottom of the track.
The distance \(y\) should be approximately 10 cm.
(b) (i) Measure and record the distance \(y\) as shown in Fig. 2.1.
\(y =\) ...................................................[1]
(ii) Estimate the percentage uncertainty in your value of \(y\).
percentage uncertainty = ...........................................................[1]
(iii) Measure and record the distance \(x\) as shown in Fig. 2.1.
\(x =\) ...................................................[1]
(iv) Calculate the radius \(R\) of the track where \(R\) is given by
$$R = \frac{x^2}{8y} + \frac{y}{2}.$$
\(R =\) ...................................................[1]
(c) (i) Place a sphere on the track as shown in Fig. 2.2.
Fig. 2.2
(ii) Release the sphere and watch the movement. The sphere will move down one side of the track and up the other side before returning, completing a cycle as shown in Fig. 2.3.
Fig. 2.3
(iii) The time taken for one complete cycle is \(T\). By timing several of these complete cycles, determine an accurate value for \(T\).
\(T =\) ...................................................[2]
(d) Reduce \(x\) by approximately 5 cm and repeat (b)(i), (b)(iii), (b)(iv) and (c).
\(y =\) ........................................................
\(x =\) ........................................................
\(R =\) ........................................................
\(T =\) ........................................................[3]
(e) It is suggested that the relationship between \(T\) and \(R\) is
$$T^2 = kR$$
where \(k\) is a constant.
(i) Using your data, calculate two values of \(k\).
first value of \(k =\) .....................................................
second value of \(k =\) .....................................................[1]
(ii) Justify the number of significant figures that you have given for your values of \(k\).
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........................................................................................................................[1]
(iii) Explain whether your results in (e)(i) support the suggested relationship.
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........................................................................................................................[1]
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ........................................................................................................................
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2. ........................................................................................................................
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3. ........................................................................................................................
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4. ........................................................................................................................
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(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. ........................................................................................................................
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2. ........................................................................................................................
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3. ........................................................................................................................
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4. ........................................................................................................................
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506
565
566
