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Transcript
Construction of capacitor and inductor Level: Secondary 6 Project aims: The main purposes of this project are to let students: 1. Familiarize with the working principles of capacitor and inductor. 2. Construct workable inductors and capacitors using simple components. Learning objectives: 1. 2. Manipulate materials, apparatus and tools for construction. Apply knowledge and principles of physics to solve problems. Task 1: Students have to construct a capacitor and an inductor by using household materials and/or elementary electrical components. Task 2: Students are asked to modify the capacitor and inductor made in Task 1 to achieve capacitance and inductance to 50nF and 1mH (without ferrite) or 10mH (with ferrite) respectively. Apparatus/Materials: Any appropriate apparatus and materials proposed by students are welcomed. Typical examples include coil, aluminum foil, connecting wires, multi-meters* (for measuring capacitance, inductance and resistance) and so on. Ferrite iron or soft iron bar can be inserted into the solenoid to increase the inductance. Students can try any suitable insulating materials like paper or plastic wrapping sheet as the dielectric of capacitor. * If the school do not have such multi-meter students may have to use other method to find the inductance and capacitance in that sense. Reference on this is shown in the Appendix. Pre-knowledge: Capacitor The capacitance of parallel plates capacitors are C 0 A d [1] where is dielectric constant, is permittivity constant equals to 8.85 10 12 Fm-1, A is overlapping area of two plates and d is separation between two plates. Inductor Solenoid inductance is roughly given by N B [2] I where N B (nl )( BA) and n is the number of turns per unit length, l is L the length of the solenoid, B is the magnetic field inside the solenoid and A is the cross-sectional area. Besides, magnetic field B of solenoid is given by B nI , where is permeability and I is current. The relative permeability is k 0 where k is relative permeability, 0 is permeability constant equal to 4 107 Hm-1. Finally, the inductance could be expressed as L n 2 lA . Questions: 1. 2. 3. 4. Using the same amount of material, why is the capacitance in a rolled up cylindrical capacitor higher than that of parallel plate? Argue without using the formula of capacitance of cylinder. A company wants to produce the capacitor with highest capacitance and lowest cost. Can you help them to design the shape and material that should be used? Inside the coil, soft iron bar or ferrite can be put into it to increase the inductance. Try other material and argue if they contain iron. Can you mathematically show that what shape of the coil can produce the maximum amount of inductance given the same length of wire? Justify your answer by wrapping a few coils. Extension: Based on your constructed capacitor and make use of a multimeter that can measure capacitance to make a digital balance. If a multimeter can measure the capacitance of the capacitor, students can make use of this multimeter to make a digital balance. The capacitor similar to Figure 5 is sensitive to pressure. Adding mass on the book will change the capacitance and it can be shown in the digital balance. By putting some known mass on the book and make a table, students can plot a graph with capacitance against mass. Putting the value of capacitance in the graph and extrapolate the value of the mass, the digital balance is ready to use. Appendix: Measuring capacitance / inductance by measuring time constant R CRO Signal Generator C Figure 9: Circuit of measuring capacitance without meter Figure 9 shows a simple RC circuit. The CRO measure the voltage across the capacitor. Signal generator can charge capacitor or switch to discharge capacitor. The equation which describes the potential difference across the capacitor VC (t ) in the circuit of Figure 9 is of the form: VC (t ) (Vo V f )e t TC V f [1] Using square wave signal with 8-volt peak-to-peak voltage, the signal generator can charge the capacitor and then discharge it. The charging cycle and the discharging cycle could be observed, as shown in Figure 10. Now assuming the power supply is +4V, then Vo would be -4V and Vf = 4V for charging cycle, and vice versa for discharging cycle. Voltage where Vo is initial voltage, Vf is final voltage and Tc is time constant, Tc = RC. Discharging Cycle Charging Cycle Time Figure 10: Charge and The resistance should be confirmed by voltmeter and ammeter. discharge cycle (Question: Why shall the resistance be measured by voltmeter and ammeter but not directly through a ohmmeter?) The resistance should be confirmed by voltmeter and ammeter so that the internal resistance of the whole circuit can be found. Compute the time constant times, as shown in Figure 11. Moving the last term to the left of the equal sign and dividing these two measurements yields: e ( t 2 t1 ) TC IC t1 , v(t1) Voltage Equation [1] can be used to solve for the time constant TC by measuring the voltage VC (t ) at two different t 2 , v(t 2 ) FC vC (t1 ) V f Time vC (t 2 ) V f Figure 11: Discharge cycle In this case, solving for the time constant TC is accomplished by taking the natural logarithm of both sides and rearranging to produce the result: TC ln( t 2 t1 v(t1 ) V f v(t 2 ) V f ) Students may also use charging cycle, but to rearrange the terms of equation [1] carefully. The time constant for this circuit is given by the equation TC RC . Students may use this equation to compute the capacitance, C. The method of finding inductance is the same by replacing capacitor with inductor. The equation of time constant is TL L / R . Measuring capacitance and inductance by measuring the phase difference Another method to measure the capacitance and inductance is by measure the phase difference. In a circuit diagram similar to Figure 9, we can measure the voltage across the resistor and across the whole signal generator. The signals can be seen in a CRO like Figure 12. A phasor diagram is constructed in Figure 13. 2 0 6 VC E 4 VR 2 Ф VC 0 -2 -4 VR E 0 2 Figure 12: CRO Image Figure 13: Phasor Diagram In Figure 12 and 13, the potential difference across resistor VR, and e.m.f. E are labeled with red and blue respectively. As a reference potential difference across capacitor VC is also included and labeled with dotted green line. The e.m.f. of the circuit is equal to the vector sum of potential difference of capacitor and resistor: E VC VR [2] The phase difference between resistor and e.m.f. is tan VC 1 [3] VR 2fCR The phase difference can be found by measuring the distance between the peak of VR and E. The phase difference is the ratio this distance and that of one period. By measuring the phase difference, the capacitance C can be found by equation [3].