You are provided with an ammeter, resistor, key, metre bridge, and other necessary apparatus. i. Connect a circuit as shown in the diagram above. ii. Close ...

Test of Practical Knowledge: Metre Bridge and Ammeter

The apparatus is connected so that the cell, key, ammeter and resistor \(R\) are joined in series to end \(A\) of the metre bridge wire, while the jockey is used to make contact with the wire at \(N\). Only the length \(AN = d\) of the bridge wire carries the current, so as \(d\) increases the resistance in the circuit rises and the ammeter reading \(I\) falls.

(ii) - (vi) Readings and table. For each contact length \(d = AN\) the key is closed, the ammeter reading \(I\) is taken, its reciprocal \(I^{-1}\) is evaluated and \(\log I^{-1}\) obtained. The results are tabulated below.

S/N	d (cm)	I (A)	I-1 (A-1)	log I-1
1	25	0.65	1.54	0.19
2	35	0.55	1.82	0.26
3	50	0.44	2.50	0.40
4	65	0.30	3.33	0.52
5	80	0.23	4.35	0.64

(vii) Graph. \(\log I^{-1}\) is plotted on the vertical axis against \(d\) on the horizontal axis and the best straight line is drawn through the points.

(viii) Slope. Taking two widely separated points on the line, \((25,\;0.20)\) and \((80,\;0.64)\):

\[ s = \frac{\Delta(\log I^{-1})}{\Delta d} = \frac{0.64 - 0.20}{80 - 25} = \frac{0.44}{55} = 8.0\times10^{-3}\ \text{A}^{-1}\,\text{cm}^{-1}. \]

(ix) Two precautions.

• The key was opened between successive readings so that the bridge wire did not heat up and change its resistance.
• Clean, tight connections were made and parallax error was avoided by reading the ammeter and the metre rule with the eye directly in line with the pointer and the scale.

(b)(i) Value of d when I = 1.5 A.

\[ I^{-1} = \frac{1}{1.5} = 0.67\ \text{A}^{-1}, \qquad \log I^{-1} = \log(0.67) = -0.17. \]

The best-fit line is \(\log I^{-1} = 8.0\times10^{-3}\,d - 0.01\). Producing this line downwards until it meets \(\log I^{-1} = -0.17\) gives

\[ d = \frac{-0.17 + 0.01}{8.0\times10^{-3}} \approx -20\ \text{cm}. \]

Because this value falls below \(d = 0\) (off the lower end of the scale), a current as large as \(1.5\ \text{A}\) cannot be obtained with this circuit: even the shortest usable length of wire keeps the current below about \(0.65\ \text{A}\).

(b)(ii) Two factors that affect the resistance of a wire.

• The length of the wire (resistance increases with length).
• The cross-sectional area (thickness or diameter) of the wire (resistance decreases as the area increases).

(The resistivity or nature of the material and the temperature of the wire also affect its resistance.)