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</div><h2>SL Paper 3</h2><div class="specification">
<p>The circuit shown may be used to measure the internal resistance of a cell.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-27_om_07.51.02.png" alt="M17/4/PHYSI/SP3/ENG/TZ2/02"></p>
</div>
<div class="specification">
<p>The ammeter used in the experiment in (b) is an analogue meter. The student takes measurements without checking for a “zero error” on the ammeter.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An ammeter and a voltmeter are connected in the circuit. Label the ammeter with the letter A and the voltmeter with the letter V.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In one experiment a student obtains the following graph showing the variation with current <em>I</em> of the potential difference <em>V</em> across the cell.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-27_om_08.05.10.png" alt="M17/4/PHYSI/SP3/ENG/TZ2/02b"></p>
<p>Using the graph, determine the best estimate of the internal resistance of the cell.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a zero error.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After taking measurements the student observes that the ammeter has a positive zero error. Explain what effect, if any, this zero error will have on the calculated value of the internal resistance in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An electrical circuit is used during an experiment to measure the current <em>I</em> in a variable resistor of resistance <em>R</em>. The emf of the cell is e and the cell has an internal resistance <em>r</em>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A graph shows the variation of \(\frac{1}{I}\) with <em>R</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the gradient of the graph is equal to \(\frac{1}{e}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the value of the intercept on the <em>R</em> axis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>