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Date: 25th March, 2010 Title: Investigating the capacitance of a parallel-plate capacitor using a reed switch Objective: To investigate the factors which affect the capacitance of a parallel-plate capacitor using a reed switch. Apparatus: – reed switch – signal generator – capacitor plates of area about 0. 24m X 0. 24 m 1 pair – polythene spacers ( 10 X 10 X 1 mm ) – polythene sheet, same area as capacitor plate 1 mm thick – battery box with 4 cells 2 – voltmeter – light-beam galvanometer – standard mass, e. g. 100g resistance substation box – CRO – Connecting leads Procedure: The reed switch 1) The reed switch was examined.
The plastic box was opened up and looked inside. 2) The yellow terminals of the reed switch module were connected to low impedance input of a signal generator. The frequency was gradually increased. If necessary, the voltage output was increased. 3) Note that a diode was connected in series to the coil inside the module. Setting up the apparatus 4) The apparatus was set up as above. The capacitor plates were separated with 4 polythene spacers placed at the corners.
The frequency and voltage of the signal generator were adjusted such that a sound was heard and the spot in the light-beam galvanometer was deflected. 5) When a signal of frequency f was applied, X vibrated between Y and Z at the same frequency. When X made contact with Y, the capacitor was charged by the d. c. supply: when X made contact with Z, it discharged through the light-beam galvanometer. 6) An essential condition for which I=Qf was stated. 7) A variable resistor was connected in series with the galvanometer to protect it from damage.
Damage may result from an accidental connection of the d. c. upply to the galvanometer. 8) If the resistance was too low, it had little effect. If it was too high, the discharge of the capacitor may be incomplete. A CRO was connected across the variable resistance to monitor the discharging current pulse. The viable resistor was adjusted to a maximum value such that each pulse fell to zero before the next one. Charge and applied p. d. 9) The signal generator was set to the maximum allowed frequency marked on module. 1 cell in the battery was connected up. The readings on the galvanometer were taken. 10) The voltage was increased in steps by connecting up more cells in the battery box.
In each case, the readings on the galvanometer were taken. 11) The sensitivity of the galvanometer was note and it was used to convert the deflection to current. The results were tabulated. Effect of plate separation 12) Without changing the voltage, the number of spacers n was increased in steps and the reading [pic] of the galvanometer were taken. The results were tabulated. Effect of area of overlap 13) Without changing the charging voltage and the number of spacers used, the area of overlap of the metal plate was charged as shown above. Relative permittivity 4) With a one-spacer separation between the plates, the reading [pic]of the galvanometer deflection was taken. 15) The spacers were replaced with a sheet of polythene of the same thickness as a dielectric. The galvanometer reading[pic]0was taken. The ratio of[pic]was taken. Precautions: • The resistance of the variable resistor should neither be very high and very low. If the resistance is too high, the charges stored in the parallel-plate capacitor may not be fully discharged, so that the measured current is not accurate, which is definitely smaller.
If the resistance is too low, it may have a chance to damage the light-beam galvanometer because of large current. • We should not assume the electromotive force provided by one battery is exactly the value which is claimed to be. As there is current flow, the voltmeter, variable resistor, light-beam galvanometer and the reed switch may draw a little current, which results in lower potential difference. Moreover, the battery may have been used for several times. It may not be able to convert chemical energy to electrical energy at the claimed rate. The p. d. provided by different battery is slightly different. The connecting wires should not touch the parallel plates. As the reading of the light-beam galvanometer will be affected if a connection wire touches one of the parallel plates. • The supplied voltage should not be too large. Otherwise, the heating effect at the contact points of the reed switch may be too large which may result to damage of the reed switch. • The frequency generated by the signal generator should not be too large. If the switching frequency is too high, the reed switch may not be sensitive enough to respond and there may not be enough time for the capacitor to undergo complete discharge. We should reset the voltmeter and the light-beam galvanometer to zero or make a zero reference point. Otherwise, the measured value is not correct. Theories: In the experiment, the reed switch allows the capacitor to be charged up and discharge rapidly. If a capacitor with capacitance C is charged up at a voltage V, the charge Q stored in it will be Q=CV. If the frequenvy at which the reed switch is operated is f, the charging and discharging process will be repeated f times per second, and the charge Q on the capacitor is delivered to the microammter at the same rate.
Assuning the capacitor is fully charged up and discharged every time, the total quantity of charge passes throgh the microammeter in a second is Qtotal = CVf. This gives the size of theoretical current I. The capitance of the capacitor can be estimated from C=I/Vf. Hence, reading of the microammeter reflects the capitance of the parallel-plate capacitor. For a parallel plate capacitor, it can be verified that the capacitance is directly proportional to area of overlap A, and inversely proportional to the seperaton of the metal plates d. i. e. [pic] here [pic] is known as permittivity of the insulating medimum (also called the dielectric) between the plated. In a particular, without the presence of dielectric, C is given by C0=[pic]0[pic]. The ratio[pic]s known as he relative premittivity of the dielectric. Discussion: The reed switch • The number of charge-discharge actions per second equals the frequency of the a. c. supply to the coil. If the value of f is so high that current pulses follow one another so rapidly that the galvanometer deflection is steady and represents the average current I through the galvanometer. A diode is connected in series to the coil inside the module to allow current to flow in one direction only and to block current in the opposite direction, so that the time of changing can equal the time of discharging. Setting up the apparatus • The reed switch operates from a signal of known frequency, i. e. 400 Hz. This causes the reed switch to oscillate rapidly between Y and Z, so the capacitor rapidly charges up from the power supply and then discharges through the microammeter. The current I indicated by the meter is equal to fQ, where f being the number of times the capacitor is discharged per unit time and Q are the charges on the capacitor when it is fully charged. For I = Qf to be correct, we assume that : a) The capacitor charges fully during the time it is connected to the power supply, and b) The capacitor discharges completely during the time it is connected to the meter Charge and applied p. d. • Frequency f = 400 Hz Galvanometer sensitivity k =19. 8 mm/µA[pic] |P. d. V/V |1. 4 |2. 8 |4. |5. 8 | |Deflection [pic]/mm |3 |9 |15 |21 | [pic] • From the graph, a straight line passes through the origin is obtained. The charge on the capacitor is directly proportional to the p. d. across it. • Slope of the graph = [pic] [pic] Effect of plate separation |Number of spacers n |4 |8 |12 |16 |20 | |[pic] |0. 25 |0. 125 |0. 083333 |0. 0625 |0. 5 | |Deflection [pic]/mm |9 |6 |5 |4 |4 | [pic] • The graph of[pic] against [pic] is a straight line. This shows that the current is proportional to[pic] and since current is proportional to the capacitance, the capacitance is inversely proportional to the plate separation. • The graph does not pass through origin, which means that when [pic]is zero there is still some capacitance. This is due to the stray capacitance which exists between the plates and the bench or some nearby conductors. Effect of area of overlap Protruding length x/cm |0 |4 |8 |12 |16 | |Area of overlap A/m2 |0. 0576 |0. 048 |0. 0384 |0. 0288 |0. 0192 | |Deflection [pic]/mm |15 |12 |11 |9 |8 | [pic] • The graph of[pic] against A is a straight line. This shows that the current is proportional to A and since current is proportional to the capacitance, the capacitance is directly proportional to the plate eparation. • The graph does not pass through origin, which means that when A is zero there is still some capacitance. This is due to the stray capacitance which exists between the plates and the bench or some nearby conductors. Relative permittivity • With polythene as a dielectric [pic]= 25 mm Without polythene as a dielectric [pic]0= 9 mm [pic] With polythene as a dielectric, C[pic][pic] [pic]0[pic]r[pic][pic][pic] Without polythene as a dielectric, C[pic][pic]0 [pic]0[pic][pic][pic]0 [pic][pic]= ([pic]0[pic]r[pic])/([pic]0[pic]) = [pic]r = relative premitivity[pic]of polythene
Sources of errors • There may be stray capacitance from the bench and the wall. Some field lines from or to the plates may actually come from or go to earth and other circuit component, such as connecting wire, which form the extra capacitor. • It is assumed that the edge effect of the plates can be ignored and all field lines between the plates are straight. In fact, the field lines curve at the edges. • The resistor may be too large so that the capacitor is not fully discharged. This will affect the calculated capacitance of the parallel-plate capacitor. The frequency generated by the signal generator has not been actually measured. This can affect the obtained capacitance of the parallel-plate capacitor. Possible Improvements • Try to keep the parallel-plate capacitor away as far as possible to avoid stray capacitance. • Try to measure the frequency using a CRO so that the exact frequency can be measured. Hence, a more accurate result of the capacitance can be obtained. • Try to monitor the p. d. across the capacitor (or resistor) with a CRO. Adjust the resistance to a value that he capacitor can be fully discharged and that the light-beam galvanometer cannot be damaged. Conclusion: There are some factors affecting the capacitance of a parallel-plate capacitor using a reed switch. These factors include plate separation, area of overlap and the existence of a dielectric. The result shown that capacitance is directly proportional to voltage supplied, inversely proportional to plate separation, directly proportional to the area of overlap. Also, the relative permittivity is equal to the ratio of current when having a dielectric in between the plates and that when having no dielectric.
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