You are provided with cells, a potentiometer, an ammeter, a voltmeter, a bulb, a key, a jockey, and other necessary materials. Measure and record the emf E ...

Answer Details

(a) Potentiometer measurement of V and I

The emf of the battery is first measured directly with the voltmeter across the battery terminals on open circuit, giving \(E = 3.0\ \text{V}\).

The circuit is connected as shown below. The key K is closed and the jockey is pressed firmly at J so that \(PJ = x\). For each length x the voltmeter reading V (across the bulb) and the ammeter reading I are recorded, and \(\log V\) and \(\log I\) are evaluated.

Observation / table of readings

x (cm)	V (V)	I (A)	log V	log I
10	0.30	0.06	-0.523	-1.222
20	0.40	0.09	-0.398	-1.046
30	0.50	0.13	-0.301	-0.886
40	0.60	0.18	-0.222	-0.745
50	0.70	0.24	-0.155	-0.620
60	0.79	0.30	-0.102	-0.523

Graph of log I against log V

A straight line of best fit is drawn through the plotted points.

Slope, s

Taking two widely separated points on the line of best fit, \((\log V_1, \log I_1) = (-0.523,\ -1.222)\) and \((\log V_2, \log I_2) = (-0.102,\ -0.523)\):

\[ s = \frac{\log I_2 - \log I_1}{\log V_2 - \log V_1} = \frac{-0.523 - (-1.222)}{-0.102 - (-0.523)} = \frac{0.699}{0.421} \]\[ s = 1.66 \]

Intercept, c (on the vertical axis)

Using the line equation \(\log I = s\,\log V + c\) with the point \((-0.102,\ -0.523)\):

\[ c = \log I - s\,\log V = -0.523 - (1.66)(-0.102) = -0.523 + 0.169 \]\[ c = -0.35 \]

Two precautions

1. The jockey was pressed on the potentiometer wire only momentarily (and the key opened between readings) to prevent heating of the wire and the cells.
2. The eye was placed directly in line with the pointer when reading the ammeter and voltmeter to avoid error of parallax.

(b)(i) Effect on the brightness of the bulb as x increases

The brightness of the bulb increases as x increases. This is because a longer length PJ of the potentiometer wire delivers a larger potential difference to the bulb, so both the voltage across the bulb and the current through it increase, raising the electrical power \(P = VI\) dissipated in the filament.

(b)(ii) Two electrical devices that do not obey Ohm's law

1. Semiconductor diode (p-n junction).
2. Thermistor.