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Fig. 1.1 shows a coil (coil X).
A student winds another coil (coil Y) tightly around coil X. A changing e.m.f. in coil X induces an e.m.f. in coil Y. The student wishes to investigate how the e.m.f. $V$ in coil Y depends on the frequency $f$ of the current in coil X. It is suggested that $V$ is directly proportional to $f$.
Design a laboratory experiment to investigate the suggested relationship. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) the measurements to be taken,
(c) the control of variables,
(d) the analysis of the data,
(e) the safety precautions to be taken.
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530
A student is investigating how the period $T$ of a simple pendulum depends on its length $l$, as shown in Fig. 2.1.
The time $t$ for 10 oscillations is recorded for a pendulum of length $l$. The period $T$ of the pendulum is determined. The procedure is then repeated for different lengths.
It is suggested that $T$ and $l$ are related by the equation $T = a l^b$ where $a$ and $b$ are constants.
(a) A graph is plotted of lg $T$ on the y-axis and lg $l$ on the x-axis. Determine expressions for the gradient and $y$-intercept in terms of $a$ and $b$. [1]
(b) Values of $l$ and $t$ are given in Fig. 2.2.
Calculate and record values of T / s, lg (l / cm) and lg (T / s) in Fig. 2.2. Include the absolute uncertainties in lg (T / s). [3]
(c) (i) Plot a graph of lg ($T$ / $s$) against lg ($l$ / cm). Include error bars for lg ($T$ / $s$). [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 uncertainty in your answer. [2]
(iv) Determine the $y$-intercept of the line of best fit. Include the uncertainty in your answer. [2]
(d) Using your answers to (c)(iii) and (c)(iv), determine values for $a$ and $b$. Include the uncertainties in your answers. You need not be concerned with the units of $a$ and $b$. [3]
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531
