A relay coil

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Circuit foundations and passive networks · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Phasors, impedance and the frequency response

Problem

A relay coil, modelled as an ideal inductor L=47 mHL = 47\,\mathrm{mH} with its winding resistance neglected, is wired in series with a separate R=330 ΩR = 330\,\Omega sense resistor. An ideal sinusoidal voltage source V‾in\underline{V}_{in} drives the series combination (inductor then resistor), and the output is taken as the phasor voltage V‾R\underline{V}_R across the resistor, measured with respect to the ground node at the far end of the resistor. ((a)) Using the impedance divider (Kirchhoff's voltage law written for phasors), derive H(jω)=V‾R/V‾inH(j\omega) = \underline{V}_R/\underline{V}_{in} and show it can be written as 1/(1+jωL/R)1/(1 + j\omega L/R). ((b)) Find the corner frequency fc=R/(2πL)f_c = R/(2\pi L) in hertz. ((c)) State ∣H∣|H| and arg⁡H\arg H at f=fcf = f_c. ((d)) Evaluate ∣H∣|H| and arg⁡H\arg H at f=10fcf = 10f_c.

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