To detect vehicles at traffic lights, wire loops with
Chapter 30, Problem 30.101(choose chapter or problem)
To detect vehicles at traffic lights, wire loops with dimensionson the order of 2 m are often buried horizontallyunder roadways. Assume the self-inductance of such aloop is L = 5.0 mH and that it is part of an LRC circuitas shown in Fig. 30-37 with C = 0.10 /xF and R = 45 O.The ac voltage has frequency / and rms voltage Vrms.(a) The frequency / is chosen to match the resonantfrequency / 0 of the circuit. Find / 0 and determine what therms voltage (VR)Tms across the resistor w ill be when/ = / 0. (b) Assume that f, C, and R never change, butthat, when a car is located above the buried loop, theloops self-inductance decreases by 10% (due to inducededdy currents in the cars metal parts). Determine by whatfactor the voltage (VR)Tms decreases in this situation incomparison to no car above the loop. [Monitoring (VR)rmsdetects the presence of a car.]FIGURE 30-37 101
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