LAB_16 - AC Impedance - Lab 16 AC Impedance "In our...

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Lab 16 177 AC Impedance Summary Investigating the relationship between alternating current (AC) and voltage leads to the concept of ac impedance. In this experiment we will measure the impedance of a variety of circuit elements in vari- ous configurations. Educational Objectives After preforming this experiment, students should be able to measure, calculate and compare impedances of various network configurations excited by sinusoidal driving forces. Background Information The three basic passive circuit elements are the resistor R , the inductor L and the capacitor C . In Figure 1, we apply the sinusoidal voltage: to each circuit element, and wait for steady state conditions. Steady state means that all transient effects after switching the signal on have died out. It is a fundamental fact when a linear circuit is driven by sinu- soidal sources, that in the steady state, all voltages and currents will also be sinusoidal and of the same frequency. "In our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience." - Niels Bohr Vt V t m ( ) cos( ) = ω
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Lab 16 178 For each of the above circuits, the current is measured after steady-state conditions have been obtained. Figure 2 shows the current and voltage waveforms associated with each of these circuit ele- ments. Note that the current and voltage in the resistor are in phase (pass through their maximum and minimum values at the same time), while the other two elements cause a ±90º phase shift between voltage and current. In the inductor, the current wave has its maximum 90º after the voltage has its maximum. We say that the inductor current lags the inductor voltage by 90º. For the capacitor, the current has its maxi- mum 90º before the voltage. Therefore, we say that in the capacitor, current leads the voltage by 90º. Resistor - In phase Inductor - Current Lags Capacitor - Current Leads Figure 2 - Sinusoidal current and voltage time relationships in the basic passive circuit elements. Left panel, resistor: no phase shift. Center panel, inductor: current lags voltage by 90º. Right panel, capacitor: current leads voltage by 90º. These graphical observations can be summarized mathematically by the following equations for the steady-state current: Figure 1: Sinusoidal voltage applied to the three basic elements. Resistor: (1) i V R t R m = cos( ) ω
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Lab 16 179 Phasors The same results are more easily described using phasors. In engineering it is common to let the symbol j denote the square root of –1, so that j 2 = –1. Using this notation, the sinusoidal voltage is just the real part of the expression . Thus the derivative of
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LAB_16 - AC Impedance - Lab 16 AC Impedance "In our...

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