To investigate the relationship between the power consumed by a torch bulb and the resistance, by measuring the potential difference across the bulb and its current.

                                                        P=kRn

       

                             Where P = IV, R =  and k and n are constants.

• In order to obtain a straight line graph to graphically represent the relationship between P and R, the following equation is derived:

                                                 lnP = nlnR + lnk.

Where n=gradient, lnk=y intercept, when lnP is plotted against lnR on the graph and         each current (I) and voltage (V) values are used to find their corresponding P and R.

Diagram 1.0: Showing setup of Equipment

                                                 

Results:  Voltage(V) and Current(I) measured. Each of them had an uncertainty of ±2%

                

Analysis:

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From Graph:

y = 3.3559 – 16.075

lnP=nlnR+ln k.

 P=kRn  ∴ P=e-16.075 × R3.3559

∴ the unit of k is :

P(W)=k ({?})R3.3559(Ω3.3559)

k= 1.04 x 10-7WΩ−3.3559

• The constants n and k are observed to be within the particular range of current and voltage, when the values of P or R are given, n and k can be used to calculate the value of R/P. The constants n and k will change according to the value of I and V.
• P and R uncertainties do not have a significant effect on n and k and can be taken as negligible. However they do affect the shape of the graph.
• The relationship between P and R is as follows:

     P∝R3.3559    ∴   P = e-16.075 R3.3559                   

• The correlation found using the lnP versus lnR graph was extremely strong, with R2 derived as being equal to 0.99784, indicating an almost perfect straight-line graph and positive correlation.

Conclusion:

From the experiment we concluded the following:

• P=1.04 x 10-7  × R3.3559   
• n = 3.3559  
• k = 1.04 x 10-7  WΩ−3.3559

To reduce the uncertainties of power and resistance, the uncertainties of voltage and current must first be reduces as they are linked. To achieve this V should have been measured more than twice at each current level. The number of current and voltage values should also be increased so as to have more values to plot on the graph. The power law in particular the formula used applies to this experiment, as lnP increases, lnR increases linearly; P is increased by the product of k and R to the power of n. This is also shown by the strong positive correlation of the graph that further shows that the power law is applied as when lnR increases, lnP increases proportionally or linearly.