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Unformatted text preview: HB, MS 12-06-2010 RL Circuits 1 RL Circuits Equipment SWS, RLC circuit board, 2 voltage sensors (no alligator clips), 2 leads (35 in) Reading Review operation of oscilloscope, signal generator, and power amplifier II 1 Introduction The 3 basic linear circuits are the resistor, the capacitor, and the inductor. This lab is concerned with the characteristics of inductors and circuits consisting of a resistor and an inductor in series (RL circuits). The primary focus will be on the response of an RL circuit to a step voltage and a voltage square wave. 2 Inductors An inductor is a 2 terminal circuit element that stores energy in its magnetic field. Inductors are usually constructed by winding a coil with wire. To increase the magnetic field inductors used for low frequencies often have the inside of the coil filled with magnetic material. (At high frequencies such coils can be too lossy.) Inductors are the least perfect of the basic circuit elements due to the resistance of the wire they are made from. Often this resistance is not negligible, which will become apparent when the voltages and currents in an actual circuit are measured. If a current I is flowing through an inductor, the voltage V L across the inductor is pro- portional to the time rate of change of I, or dI dt . We may write V L = L dI dt , (1) where L is the inductance in henries (H). The inductance depends on the number of turns of the coil, the configuration of the coil, and the material that fills the coil. A henry is a large unit of inductance. More common units are the mH and the H. A steady current through a perfect inductor (no resistance) will not produce a voltage across the inductor. The sign of the voltage across an inductor depends on the sign dI dt and not on the sign of the current. A positive current that is decreasing will produce a negative voltage across an inductor. If an inductor has a resistance R L the voltage across the inductor will be V L = L dI dt + IR L . (2) The most important specification for an inductor is its maximum current rating. 3 RL Circuits A series RL circuit with a voltage source V(t) connected across it is shown in Fig. 1. The voltage across the resistor and inductor are designated by V R and V L , and the current around the loop by I. The signs are chosen in the conventional way. I is positive if it is in the direction HB, MS 12-06-2010 RL Circuits 2 of the arrow. Kirchoffs law, which says that the voltage changes around the loop are zero, may be written V L + V R = V. (3) Assuming R L = 0 and letting V L = L dI dt and V R = IR Eq.(3) becomes L dI dt + RI = V. (4) The solution to the homogeneous equation (V(t)=0=a short circuit) is I ( t ) = I e- t L/R , where I is the current through the circuit at time t=0. This solution leads immediately to V R = I Re- t L/R and V L =- I Re- t L/R . The homogeneous solution decays exponentially with a time constant of L/R....
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- Spring '11