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In this experiment, you will investigate the current in an electrical circuit.
(a) Connect the circuit shown in Fig. 1.1.
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F, G and H are crocodile clips. The crocodile clip G is used as a movable contact. Position G approximately half-way along the resistance wire.
(b) (i) The distance between F and G is x, as shown in Fig. 1.1. Measure and record x.
$x = \text{............................... cm}$ [1]
(ii) Close the switch.
(iii) Record the ammeter reading I.
$I = \text{...............................}$ [1]
(iv) Open the switch.
(c) Vary x and repeat (b) until you have six sets of values for x and I.
[8]
(d) (i) Plot a graph of 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.
$\text{gradient} = \text{...............................}$
$\text{y-intercept} = \text{...............................}$ [2]
(e) The quantities I and x are related by the equation
$$I = Sx + T$$
where S and T are constants.
Use your answers from (d)(iii) to determine the values of S and T. Give appropriate units.
$S = \text{...............................}$
$T = \text{...............................}$ [2]
(f) The resistance per unit length r of the resistance wire can be found from
$$r = \frac{PS}{T}$$
where $P = 15\Omega$ (the resistance of resistor P).
Calculate r in $\Omega \text{cm}^{-1}$.
Give your answer to a suitable number of significant figures.
$r = \text{...............................\Omega cm}^{-1}$ [2]
563
565
551
(a) (i) Set up the apparatus as shown in Fig. 2.1. Use some of the Blu-Tack to fix the pivot to the empty beaker.
(ii) The rods of the clamps act as stops to prevent the metre rule tilting too far. Adjust them so that one is approximately 3 cm higher than the pivot and the other is approximately 3 cm lower than the pivot.
(iii) Position the metre rule with its 50.0 cm mark at the pivot. If necessary, add Blu-Tack to one end of the rule to balance it.
(b) You are provided with two glass spheres fixed to string loops.
(i) Suspend the larger sphere from the metre rule at a distance of 10.0 cm from the pivot. Balance the rule by suspending the other sphere a distance $x_1$ from the pivot, as shown in Fig. 2.2.
(ii) Measure and record $x_1$.
$x_1$ = .................................................... cm [1]
(c) Immerse the larger sphere in water at a distance of 10.0 cm from the pivot, as shown in Fig. 2.3. Balance the rule by moving the smaller sphere. Measure and record the distance $x_2$.
$x_2$ = .................................................... cm [1]
(d) (i) Repeat (b) with the spheres changed around, with the smaller sphere suspended at a distance of 40.0 cm from the pivot, as shown in Fig. 2.4.
$x_1$ = ................................................... cm [1]
(ii) Immerse the smaller sphere in water at a distance of 40.0 cm from the pivot, as shown in Fig. 2.5. Balance the rule by moving the larger sphere. Measure and record $x_2$.
$x_2$ = ................................................... cm [1]
(e) It is suggested that the relationship between $x_1$ and $x_2$ is
$$x_1 = k(x_1 - x_2)$$
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 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) Measure and record the diameter $D$ of the smaller sphere.
$D$ = .................................................. cm [2]
(ii) Estimate the percentage uncertainty in your value of $D$.
percentage uncertainty = .................................................. [1]
(iii) Calculate the volume $V$ of the smaller sphere, where $V = \frac{\pi D^3}{6}$.
$V$ = ..................................................cm$^3$ [1]
(iv) The mass $M$ of the smaller sphere is given by $M = k\rho V$ where $\rho = 1.0 \text{ g cm}^{-3}$. Using one of your values of $k$, calculate $M$.
$M$ = .................................................. g [1]
(g) (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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541
591
536
