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| These are equations describing capacitance and inductance. The board shows both differential and integrated forms of the definitions. Then the Energies were derived from the more elementary equations. This all should be review from Physics 4B: Electricity and Magnetism . |
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| We were supposed to determine what a voltage vs. time graph would look like if the current was given. First segment has a higher slope than the second and the third segment is an exponential curve |
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This was a problem given in class. We were to re draw the circuits with open circuit in place of the capacitors and then find the energy across the 2mF capacitor. |
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On top are driving voltages [v(t)] and on bottom are the corresponding predicted current graphs [i(t)]. The sine wave becomes a cosine wave and the triangle wave becomes a square wave. The 2nd is the derivative of the first.
During the Lab portion we were to build this circuit and measure the voltages across each element.
blue wires read the voltage across the resistor and the current is calculated from that. red and white wires deliver signal voltages (sin wave / triangle wave)
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| Blue is [vr(t)], orange is Vin(t), blue is Ir(T) |
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| Same coloring conventions |
Each of the graphs look as predicted in general (square waves had curved edges with a slope that was not infinite during charging and discharging phases ). There was a pi/2 phase shift from the original driving voltage and the voltages across the capacitors are the derivative of the driving voltages. Please note that the volts per division might have not been consistent for each reading which can alter the perceived relationships between the amplitude of these graphs.
In summary we reviewed capacitance and inductance and saw how each element affects alternating currents
