You are provided with a variable d.c. power supply E, a \(2\propto\) standard resistor, a key, an ammeter, a voltmeter and other necessary materials. i. Set...

(a) Table of readings

For each value of \(E\) the voltmeter reading \(V\) and the corresponding ammeter reading \(I\) are recorded, and the reciprocals \(V^{-1}\) and \(I^{-1}\) are evaluated:

S/N	\(E\)/V	\(I\)/A	\(V\)/V	\(V^{-1}\)/V\(^{-1}\)	\(I^{-1}\)/A\(^{-1}\)
1	1.5	0.30	0.80	1.250	3.333
2	3.0	0.50	1.40	0.717	2.000
3	4.5	0.70	2.00	0.500	1.429
4	6.0	0.90	2.50	0.400	1.111
5	7.5	1.10	3.00	0.333	0.909

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

\(V^{-1}\) is plotted on the vertical axis and \(I^{-1}\) on the horizontal axis, both axes starting from the origin \((0,0)\). A best straight line is drawn through the plotted points:

(ix) Slope of the graph

Two widely-separated points are read off the best line, \((I^{-1}_1, V^{-1}_1) = (0.26,\ 0.800)\) and \((I^{-1}_2, V^{-1}_2) = (1.24,\ 3.333)\):

\[ s = \frac{\Delta V^{-1}}{\Delta I^{-1}} = \frac{V^{-1}_2 - V^{-1}_1}{I^{-1}_2 - I^{-1}_1} = \frac{3.333 - 0.800}{1.24 - 0.26} = \frac{2.53}{0.98} \approx 2.6. \]

(x) Intercept on the vertical axis

Where the best line meets the \(V^{-1}\) axis (at \(I^{-1} = 0\)):

\[ e \approx 0.04\ \text{V}^{-1}. \]

(xi) Two precautions

• Ensured all terminals were clean and every connection was tight, and checked for and corrected any zero error on the voltmeter and ammeter.
• Opened the key immediately after each pair of readings was taken to avoid heating the resistor and running down the cell, and read both meters with the eye directly in line with the pointer to avoid parallax error.

(b)(i) Two methods of producing an electric current

• Chemical action in cells, accumulators or fuel cells (chemical energy converted to electrical energy).
• Electromagnetic induction using a generator or dynamo (mechanical energy converted to electrical energy). Solar/photocells and thermocouples are also acceptable.

(b)(ii) Value of \(R\)

The two resistors \(R\) are connected in parallel:

\[ \frac{1}{R_e} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \quad\Rightarrow\quad R_e = \frac{R}{2}. \]

This parallel combination is in series with the \(2\ \Omega\) standard resistor, and the effective (total) resistance of the circuit is \(4.0\ \Omega\) with negligible internal resistance:

\[ \frac{R}{2} + 2 = 4 \quad\Rightarrow\quad \frac{R}{2} = 2 \quad\Rightarrow\quad R = 4.0\ \Omega. \]