You are provided with a constantan wire, a2 \(\Omega\)standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus. Measure and...
Question 1 Report
You are provided with a constantan wire, a2 \(\Omega\)standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus.
- Measure and record the emf of the accumulator provided
- Connect a circuit as shown in the diagram above.
- Close the key, read and record the ammeter reading l\(_{o}\) when the crocodile clip is not in contact with the Constantan wire.
- Open the key with the clip making contact with the wire, when d=90cm, close the key. Read and record the ammeter reading l.
- Evaluate d\(^{_1}\)
- Repeat the procedure for four other values of d=80, 70, 60, and 50 cm
- In each case, read and record the ammeter reading and evaluatre d\(^{_1}\).
- Tabulate your readings.
- Plot a graph with I on the vertical axis and d\(^{_1}\) on the horizontal aXIS.
- Determine the slope, S of the graph and its intercept, c, on the vertical axis.
- Evaluate k = \(\frac{c}{s}\)
- Using your graph, determine the current I when d=55cm.
- State two precautions taken to obtain accurate results.
(b)i. Explain what is meant by the potential difference between two points in an electric circuit.
ii. State two factors on which the resistance of a wire depends.
Answer Details
Test of practical knowledge: current through a length of constantan wire
The circuit
The accumulator \(E\), key \(K\), ammeter \(A\), standard resistor \(R = 2\,\Omega\) and the length \(d\) of constantan wire (tapped by the crocodile clip) are joined in series as shown.
Readings recorded before the main experiment
- e.m.f. of the accumulator, \(E = 2.0\ \text{V}\)
- ammeter reading with the clip off the wire, \(I_0 = 0.90\ \text{A}\)
Table of readings
| \(d/\text{cm}\) | \(I/\text{A}\) | \(d^{-1}/\text{cm}^{-1}\) |
|---|---|---|
| 90.0 | 0.21 | 0.0111 |
| 80.0 | 0.23 | 0.0125 |
| 70.0 | 0.25 | 0.0143 |
| 60.0 | 0.29 | 0.0167 |
| 50.0 | 0.34 | 0.0200 |
Graph of \(I\) against \(d^{-1}\)
Slope of the graph
Two points are taken on the line of best fit:
\((d^{-1}_1, I_1) = (0.0060\ \text{cm}^{-1},\ 0.13\ \text{A})\) and \((d^{-1}_2, I_2) = (0.0240\ \text{cm}^{-1},\ 0.40\ \text{A})\).
\[ S = \frac{\Delta I}{\Delta (d^{-1})} = \frac{0.40 - 0.13}{0.0240 - 0.0060} = \frac{0.27}{0.0180} = 15\ \text{A}\,\text{cm} \]Intercept on the vertical axis
Where the line of best fit cuts the \(I\)-axis (at \(d^{-1} = 0\)):
\[ c = 0.04\ \text{A} \]Evaluation of \(k\)
\[ k = \frac{c}{S} = \frac{0.04}{15} = 2.67\times 10^{-3}\ \text{cm}^{-1} \]Current when \(d = 55\ \text{cm}\)
\(d^{-1} = \dfrac{1}{55} = 0.0182\ \text{cm}^{-1}\). Reading up from \(0.0182\ \text{cm}^{-1}\) to the line of best fit and across to the \(I\)-axis:
\[ I = 0.31\ \text{A} \]Two precautions
- The key was opened immediately after each reading so that the wire did not heat up (which would change its resistance) and the accumulator did not run down.
- Clean, tight terminal connections were used and the zero error of the ammeter was noted and corrected before each reading.
(b)(i) Potential difference between two points
The potential difference between two points in an electric circuit is the work done (energy converted from electrical form to other forms) in moving one coulomb of positive charge from one point to the other. It is measured in volts, where \(1\ \text{V} = 1\ \text{J C}^{-1}\).
(b)(ii) Two factors on which the resistance of a wire depends
- The length of the wire (resistance increases with length).
- The cross-sectional area of the wire (resistance decreases as the area increases).
(It also depends on the material/resistivity of the wire and on its temperature.)
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