Although we may consider the power outlets in our homes to be nearly ideal voltage sources, a variety of influences in and around the home can cause departures from the nominal 60 Hz, 110–120 V root-mean-square (rms) of the North American grid. Even without instrumentation, we can see that a large motor starting from rest can be sufficient to cause lights to dim momentarily (voltage sag). This dimming is due to the inrush current drawn by a stationary motor, which may be several times the current drawn at operating speed. We prepared a voltage monitoring system using a voltage divider, the construction details of which we omit in the interest of safety.

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Analysis of 10 trials yielded average values of b, c, and d (with 95% confidence intervals) to be b = 0.9803 ± 0.0011, c = 0.0718 ± 0.0014, and d = 12.31 ± 0.67 s−1 with a reduced χ2 of 0.195. The reduced χ2, or chi-square per degree of freedom, is simply the chi-squared divided by the number of degrees of freedom. In general, a reduced chi-squared of one is considered ideal. The variable d represents the characteristic time for the voltage to return to its equilibrium value, and is therefore indicative of the angular acceleration of the drill. The variable c provides a measure of the peak load the drill places on the circuit, and b reflects the steady state load for the freely running drill.

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Hugh D.
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and
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,
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, 11th ed. (
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,
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,
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1115
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8.
Solutions to equations such as this can be found in a standard textbook on mathematical physics
, e.g.,
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Arfken
,
Hans J.
Weber
, and
Frank E.
Harris
,
Mathematical Methods for Physicists
,
7th ed. (
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,
Waltham, MA 02451
), Sec. 7.2.
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