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...

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.

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(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.)