You are provided with a voltmeter V, a chemical cell/ battery E; two standard resistors R, and R a potentiometer a key K a jockey, and other necessary mater...

Circuit

The circuit is connected as shown, with the cell E and key K driving the potentiometer wire AB, and the voltmeter V connected across the length AC = x.

Table of readings

With the key K closed, the jockey is placed on the wire at C so that AC = x, and the voltmeter reading V is taken for each length. The reciprocals \(x^{-1}\) and \(V^{-1}\) are then evaluated.

\(x\,/\,\text{cm}\)	\(V\,/\,\text{V}\)	\(x^{-1}\,/\,\text{cm}^{-1}\)	\(V^{-1}\,/\,\text{V}^{-1}\)
20	0.15	0.050	6.667
30	0.20	0.033	5.000
40	0.30	0.025	3.333
50	0.40	0.020	2.500
60	0.50	0.017	2.000
80	0.60	0.013	1.667

Graph of \(V^{-1}\) against \(x^{-1}\)

The graph of \(V^{-1}\) (vertical axis) against \(x^{-1}\) (horizontal axis) is a straight line passing through the origin.

(a) Slope of the graph

Taking two widely separated points on the line of best fit, \((0.050,\;6.667)\) and \((0.013,\;1.667)\):

\[ s = \frac{V_2^{-1}-V_1^{-1}}{x_2^{-1}-x_1^{-1}} = \frac{6.667-1.667}{0.050-0.013} = \frac{5.000}{0.037} = 135.1\ \text{cm}\,\text{V}^{-1} \]

(b) Intercept on the vertical axis

The line of best fit passes through the origin, so the intercept on the vertical axis is

\[ c = 0 \]

Two precautions

• Tight, clean connections at all terminals were ensured before taking readings.
• The key K was opened between successive readings so that the wire did not heat up.

(b)(i) Two devices in which Ohm's law does not apply

• A semiconductor diode (rectifier).
• A thermionic (vacuum) diode/valve.

(b)(ii) Current in each parallel resistor

A total current of \(1\ \text{A}\) is supplied to \(2\ \Omega\) and \(3\ \Omega\) in parallel. The current divides in the inverse ratio of the resistances:

\[ I_{2\Omega} = 1 \times \frac{3}{2+3} = \frac{3}{5} = 0.6\ \text{A} \] \[ I_{3\Omega} = 1 \times \frac{2}{2+3} = \frac{2}{5} = 0.4\ \text{A} \]

Therefore \(0.6\ \text{A}\) flows through the \(2\ \Omega\) resistor and \(0.4\ \text{A}\) through the \(3\ \Omega\) resistor.