You are provided with a battery of e.m.f, E, a standard resistor, R, of resistance 2 \(\Omega\), a key, K, an ammeter, A, a jockey, J, a potentiometer, UV, ...
You are provided with a battery of e.m.f,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 \(I^1\).
(vi) 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 \(I^1\).
(vii) Tabulate the results
(ix) Plot a graph with d on the vertical axis and I on the horizontal axis stalling both axes from the origin (0,0).
(x) Determine the slope, s, of the graph.
(xi) From the graph determine the value \(I_1\), of I when d = 0. (ci) Given that=s, calculate 8.
(xii) State two precautions taken to ensure accurate results.
(xii) Given that \(\frac{E}{\delta}\) = s, calculate \(\delta\).
(b)(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 of0.75 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.
(a) Potentiometer experiment
(i) The e.m.f. of the battery is:
\[E=2.0\ \text{V}\]
With the jockey at \(U\), the ammeter reading is:
\[i=1.00\ \text{A}\]
(ii) Table of results
Distance, \(d\) (cm)
Current, \(I\) (A)
\(I^{-1}\) (A−1)
30.0
0.769
1.30
40.0
0.714
1.40
50.0
0.667
1.50
60.0
0.625
1.60
70.0
0.588
1.70
As \(d\) increases, \(I\) decreases.
(iii) Graph of \(d\) against \(I^{-1}\)
A straight-line graph of d against I⁻¹, with both axes beginning at the origin.
(iv) Slope of the graph
Using two widely separated points on the straight line, \((1.20\ \text{A}^{-1},20.0\ \text{cm})\) and \((1.70\ \text{A}^{-1},70.0\ \text{cm})\):
The key was closed only while taking a reading, to prevent heating of the potentiometer wire and consequent change in resistance.
The jockey was touched lightly on the wire and not pressed hard, to ensure good contact without damaging the wire.
(b)
(i) The resistance of a uniform wire is given by
\[R=\rho\frac{l}{A}.\]
\(R\) is the resistance of the wire, \(\rho\) is the resistivity of the material, \(l\) is the length of the wire, and \(A\) is its cross-sectional area.
The key was closed only while taking a reading, to prevent heating of the potentiometer wire and consequent change in resistance.
The jockey was touched lightly on the wire and not pressed hard, to ensure good contact without damaging the wire.
(b)
(i) The resistance of a uniform wire is given by
\[R=\rho\frac{l}{A}.\]
\(R\) is the resistance of the wire, \(\rho\) is the resistivity of the material, \(l\) is the length of the wire, and \(A\) is its cross-sectional area.
