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a
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You are provided with a battery of emf, E, a standard resistor, R, of resistance 2 \( \Omega \), a key, K, an ammeter, A, a jockey, J, a potentiometer, UV, and some connecting wires. (i) Measure and record the emf, E, of the battery. (ii) Set up the circuit as shown in the diagram above with the key open. (iii) Place the jockey at the point, U, of the potentiometer wire. Close the key and record the reading, i, of the ammeter. (iv) Place the jockey at a point T on the potentiometer wire UV such that d=UT=30.0 cm. (v) Close the circuit, read and record the current, I, on the ammeter. (vi) Evaluate I. (vii) Repeat the experiment for four other values of d=40.0 cm, 50.0 cm, 60.0 cm and 70.0 cm. In each case, record I and evaluate. (viii) Tabulate the results. (ix) Plot a graph with d on the vertical axis and \( I^{-1} \) on the horizontal axis starting both axes from the origin (0,0). (x) Determine the slope, s, of the graph. (xi) From the graph determine the value \( I_{0} \) of I when d=0. (xii) Given that \( \frac{E}{\delta}=s \), calculate \( \delta \). (xiii) State two precautions taken to ensure accurate results.
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b
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(i) Write down the equation that connects the resistance, R, of a wire and the factors on which it depends. State the meaning of each of the symbols. (ii) An electric fan draws a current of 0.75 A in a 240 V circuit. Calculate the cost of using the fan for 10 hours if the utility rate is $0.50 per kWh.
