Analysis of a d.doc

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University of Toronto Scarborough
Physics and Astrophysics
P H Y B20

Analysis of a dArsonval meter and Power dissipation in a black box The following experiment was conducted to analyze a dArsonval meter and its effects of its internal resistance while calculating voltage and ammeter. The analysis shows that a dArsonval meters deflection is directly proportional to the current supplied to the meter. By the using Kirchoffs and Ohms I have shown that it is possible to calculate the internal resistance of a dArsonvol meter. The resistance of the meter that I calculated was 4.3e4. The experimental reading show that the meter readings and the actual voltmeter do not match once connected to a black box. The voltmeter and the dArsonval meter reading differed by 1.8V. Hence, it can be said that a dArsonval meter is no an accurate device to calculate voltage. The second part of this experiment dealt with the power dissipation across a load resistor, connected to a black box. The experiment shows a non-linear relationship of power dissipation and a resistor in a circuit. The maximum power is dissipated when the load resistor resistance is equivalent to the overall resistance of the circuit. Introduction The DArsonval meter is extremely also called a galvanometer (galvo for short) , is a device that consists which responds to a change in current by a movement needle. The galvo consists of a magnetic field generated by two magnets, with a pivot wire between them. This experiment shows the current across the galvo is directly proportional to the deflection across of the meter. This calibration can also be used to calculate appropriate values of deflection and the corresponding. While considering the movement one also has to consider the resistance of the galvo itself. This resistance is due to the coil of wire inside the galvo. The experiment relates this resistance as: Ri= R Rs/p -s p where Ri is the resistance of the galvo, Rs and Rp are resistances connected in a circuit. As galvo is a sensitive meter it is used in measuring temperature difference between two points. The above equation and the following experiment can be used while making calibration curves for heat and deflection. Another important aspect of this experiment was calculating the power, resistance and voltage across a black box. A black box is a circuit whose components are unknown; hence resistances or voltage cannot be calculated. A similar case would be resistances of a solar cell and the voltage across it. Although factor specifications do point to the appropriate energy is lost due to heat or inefficiency. The following method can be employed to find the respective resistance and voltage. The experiment uses the Thevinins Theorem to find the respective resistance and voltage of the black box. As mentioned earlier the experiment also analyzes the relationship between a resistor and the power dissipated across it. The method can be put in to practice in calculating the power dissipation in an electrical component. Experiment and Results To calculate the resistance of the meter I used the following apparatus: 1. 1 Variable Resistor (Max R = 10e3) 2. 1 Variable Resistor (Max R= 100e3) 3. 1 Digital Multi Meter 4. 1 1.2V power source 5. 1 dArsonvol meter (Lab Code #9) (Max Deflection 25) For a galvo to work it necessary that it is connected with a resistor, as the galvo is extremely sensitive and otherwise it might damage the galvo as well. To calculate the required resistor for a full-scale deflection I arranged the circuit as follows fig(A.1). It was important that I place my galvo on a smooth plane in order to prevent unnecessary deflection. The Rs had a maximum value of 100e3and Was connecter in series with the galvo with a resistance of (Ri). The resistor was to a maximum value of 100e3 Fig (A.1) to prevent the galvo from burning out. The resistance was slowly decreased in order for the galvo pointer to reach a maximum value of 25. The table(Table A.1) shows the effect of decreasing resistance and the galvo deflection. A The resulting maximum deflection occurred at a resistance of: Rs = (4.3e4 + 430) S.No Rs/ Theta/ 1. 90,000 14.5 2. 7.00E+04 16.3 3. 6.00E+04 19.5 4. 5.00E+04 22 5. 4.40E+04 23 Table (A.1) 7. 4.30E+04 25 (FSD) Now that I had the required FSD deflection resistance (Rs), I connected another variable resistor Rp in parallel to the galvo. This resistor was varied until the galvo read half scale deflection of 12.5. This also meant that the current was divided equally in resistance Rp and the galvo as we can see from the table(Table A.1) that current is directly proportional to the deflection, because as the resistance decreases the current increases. Therefore: = k * I eq(1) fsd fsd when deflection is halved: fsd2 = k * I i taking constants from both sides: Ifsd2*Ii..eq(2) Hence the current would be halved when a the deflection is halved. The setup for a half scale is as shown in fig (Fig A.2): The deflection variation with respect to deflection is shown in A table (Table A.2) S.No Rp/Ohms Theta Fig (A.2) 1 1.00E+04 19.5 2 100 6 3 200 10 Table (A.2) 4 30 12.5 Rp= (30.0 + .3) The value measured of R wap 30.
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