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Physics and Astrophysics
P H Y B20

The following experiment deals with the working relationship of the dArsonval meter and different components of an electrical circuit. The experiment also analyzes the power dissipated in a circuit of unknown resistance and power supply. The experiment takes into account the internal resistance of a simple dArosonval meter and using the latter I have deduced how the dArosnonval meter relates to resistors of known resistances, by using Kirchoffs and Ohms laws. The experiment also shows how half and full-scale deflection relate in a ratio of 2:1, when the dArosnvol meter setup to measure current and voltage respectively. The experimental reading for the DArsonvol meter was hence calculated to be 4.3e4 ohms. The experiment also illustrates how deflection () is directly proportional to current (I). Using the various equations and result, I have shown how dArsonval meter can be used as a voltmeter and how it can be used to deduce the components of a black box, using Thevenins theorem. The calculated resistance of the black box using dArsonvol meter was 14919 ohms, which was close enough to the actual value of 1500 ohms. My experiment also deals with the relationship of power across a resistance load connected to a black box circuit. The experiment shows how thw 1 Introduction A dArsonval meter 2 Experiment and Result The experiment can be divided in four parts for easier understanding. The experiments consists of : Part A In this part I tried to find a value for the internal resistance of a dArosonval meter. Two circuits were constructed for this part of the experiment. The apparatus for to find the internatl resistance of a aArsonvol meter is as follows: 1. 1 1.2 VOLT Power supply 2. 1 Variable reisistor of a maxmmum value of 10kohm. 3. 1 Variable resistor of a maximum value of 10kohm. 4. 1 dArosonvol meter with minimum value of 0 and maximum value of 25. The meter pointer deflected from left to right. It was very important that I measured my readings on a flat plane so as not to affect the deflection of the sensitive meter. The meter, in general, is very sensitive and it was very important that I handled it accordingly. The galvo can be setup both as an ammeter and a voltmeter. When a galvo is setup as an ammeter, a resistor or a shunt resistor is connected with it in parallel, to prevent the galvo from burning out. A galvo can also be setup as a voltmeter by connecting a resistor in series with a resistor, which is also called a multiplier. This increases the resistance of the circuit hence voltage can be measured accurately. Another property of a galvo that helped me in my calculation was the how the FSD remains unchanged for any particular circuit connection. Which implies that the current at which FSD occurs is constant. I used these applications and properties of the galvo to relate internal resistance (Ri) of the galvo and the resistances connected with it in series and parallel respectively. As mentioned earlier, due to the meters high sensitivity, it was important that I connected a resistor to the galvo in order to calculate its full scale deflection ( FSD). As I did not had no formal data to calculate the FSD I had to connect a variable resistor to deduce the FSD. The resistor was connected in series with the galvo as shown in figure (Fig A.1). This setup effectively the converts the meter into a voltmeter. The following setup did demonstrate a random error. This is mainly because due to the mechanical friction in the galvo. This is something that could not e helped. Another kind of error that can occur is the variation in deflection due to change in temperature. To avoid this I, took regular breaks between measurements. 3 The variable resistance of Rs was gradually increased to as to fnd the FSD of the galvanometer. The table (Table (A.1)) shows the results obtained. S.No Rs/ Theta/ 1. 90,000 14.5 2. 7.00E+04 16.3 3. 6.00E+04 19.5 22 4. 5.00E+04 A 23 5. 4.40E+04 7. 4.30E+04 25 (FSD) Table A.1 Fig (A.1) As the above table shows that FSD, 25, of the galvo occurs at a resistance (Rs) of 43.0k. Hence: Rs = (43.00 + .04) k The uncertainty in the above calculation is possibly due to the overheating of the electrical connections. Although, I did try to minimize this systematic error, but I suppose such error cant be helped. Other source of error might have occurred while reading a the galvo, i.e a parallex error. I tried to avoid this error, by viewing the galvo needle perpendicularly to its postion. The above table (Table A.1) suggest how a galvo responds to a particular change in resistance. As I decrease the resistance the current across the resistor (Ri) increases hence the deflection of the meter increases. Hence mathematically: = kI... (1) Where is the deflection, I represents current and k is the constant. 4
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