Electric Motor Control
Electric Motor Control
10th Edition
ISBN: 9781133702818
Author: Herman
Publisher: CENGAGE L
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Chapter 40, Problem 4SQ

When the rotor and stator fields lock into step, why may the reading of the AC ammeter decrease?

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Consider the homogeneous RLC circuit (no voltage source) shown in the diagram below. Before the switch is closed, the capacitor has an initial charge go and the circuit has an initial current go. R w i(t) q(t) C н After the switches closes, current flows through the circuit and the capacitor begins to discharge. The equation that describes the total voltage in the loop comes from Kirchoff's voltage law: di(t) L + Ri(t) + (t) = 0, dt (1) where i(t) and q(t) are the current and capacitor charge as a function of time, L is the inductance, R is the resistance, and C is the capacitance. Using the fact that the current equals the rate of change of the capacitor charge, and dividing by L, we can write the following homogeneous (no input source) differential equation for the charge on the capacitor: ä(t)+2ag(t)+wg(t) = 0, (2) where R a 2L and w₁ = C LC The solution to this second order linear differential equation can be written as: where 81= q(t) = Ae³¹- Bel 82 = (3) (4) (5)
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