**Question:**

*A student wishes to investigate how the resistance R of a light-dependent resistor varies with the distance d from an intense light source.*

*It is believed that the relationship between R and d is*

*R = kd ^{n}*

*where k and n are constants.*

*Design a laboratory experiment to test the above relationship. The light-dependent resistor has a resistance of 100 Ω when it is in bright light and a resistance of 500 kΩ when no light falls on it.*

*You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to*

*(a) the procedure to be followed,*

* (b) the measurements that would be taken,*

* (c) the control of variables,*

* (d) how the data would be analysed,*

* (e) any safety precautions that you would take.*

**Solution:**

In this experiment, ‘d’ is the independent variable and ‘R’ is the dependent variable. A variable which needs to be kept constant is the power of the light source (this can be achieved by connecting an ammeter in the light source circuit together with a rheostat and then adjusting the rheostat during the experiment to keep the current constant).

The apparatus will be set up as per diagram and light source will be turned on. Distance d will be measured using a meter rule and it will be recorded. The resistance R of the LDR corresponding to this value d will also be measured using an ohm meter.

While measuring d, it should be ensured that parallax error is avoided. One way to do this is to place the LDR and the light source over a meter-rule fixed to the bench and then the light source can be moved over the meter rule (along it) to vary d. In this way, distance between LDR, the light source and the meter rule will be decreased enough to avoid parallax error. The above procedure will be repeated until we have at least 6 different readings for R and d.

The readings will be tabulated and values of lg(R) and lg(d) will be calculated.

R = kd^{n }=> lg(R) = lg(k) + nlg(d)

A graph of lg(R) against lg(d) will be plotted. If the suggested relation is correct, then the graph will be a straight line. It will be possible to find the value of k using:

K = 10^{y-intercept }

and value of n by calculating the gradient of the graph.

The experiment must be performed in a dark room where there are no other light sources than the one being used in the experiment. Ohm-meter must be able to measure resistances in the range 50Ω to 500KΩ.

The light source may be very bright and may therefore affect experimenter’s eyes. So goggles must be worn throughout the experiment.