You are provided with a constantan wire, a 2\(\Omega\) standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus. Measure an...
Question 1 Report
You are provided with a constantan wire, a 2\(\Omega\) standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus.
- Measure and record the e.m.f.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 I = 90cm, close the key. Read and record the ammeter reading /. Evaluate l\(^{-1}\).
- Repeat the procedure for l= 80, 70, 60 and 50cm.
- In each case, read and record the ammeter reading and evaluate l\(^{-1}\). Tabulate your readings.
- Plot a graph of l on the vertical axis against l\(^{-1}\) 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 / = 55cm.
- State two precautions taken to ensure 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 resistance wire depends.
Answer Details
Test of Practical Knowledge – Electricity
Circuit diagram
Measurements recorded
- E.m.f. of the accumulator, \(E = 2.0\ \text{V}\)
- Ammeter reading with the clip not in contact with the wire, \(I_{o} = 0.65\ \text{A}\)
Table of readings
| \(l\) (cm) | \(l^{-1}\) (cm\(^{-1}\)) | \(I\) (A) |
|---|---|---|
| 90 | 0.0111 | 0.70 |
| 80 | 0.0125 | 0.75 |
| 70 | 0.0143 | 0.80 |
| 60 | 0.0167 | 0.85 |
| 50 | 0.0200 | 0.90 |
Graph of \(I\) against \(l^{-1}\)
Slope of the graph
Taking two widely spaced points on the line of best fit, \((l^{-1}_{1},\,I_{1}) = (0.0100,\ 0.69)\) and \((l^{-1}_{2},\,I_{2}) = (0.0200,\ 0.91)\):
\[ s = \frac{\Delta I}{\Delta (l^{-1})} = \frac{0.91 - 0.69}{0.0200 - 0.0100} = \frac{0.22}{0.0100} = 22.0\ \text{A cm} \]Intercept on the vertical axis
Extending the line of best fit back to \(l^{-1} = 0\), it cuts the \(I\)-axis at
\[ c = 0.47\ \text{A} \]Evaluate \(k = \dfrac{c}{s}\)
\[ k = \frac{c}{s} = \frac{0.47}{22.0} = 0.021 \]Current \(I\) when \(l = 55\ \text{cm}\)
\[ l^{-1} = \frac{1}{55} = 0.0182\ \text{cm}^{-1} \]Reading this value on the horizontal axis and going up to the line of best fit:
\[ I = c + s\,(l^{-1}) = 0.47 + 22.0 \times 0.0182 = 0.87\ \text{A} \]Two precautions
- The key was opened (removed) immediately after each reading was taken, to prevent heating of the constantan wire and to conserve the accumulator.
- The terminals and crocodile-clip contacts were kept clean and the connections firmly tightened to avoid contact resistance, and the ammeter was read with the eye directly above the pointer to avoid parallax.
(b)(i) Potential difference between two points
The potential difference between two points in an electric circuit is the work done 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 resistance wire depends
- The length of the wire – resistance increases with length \((R \propto l)\).
- The cross-sectional area (thickness) of the wire – resistance decreases as the area increases \(\left(R \propto \dfrac{1}{A}\right)\).
(It also depends on the resistivity/nature of the material and on the temperature of the wire.)
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