HWelectricv1practice

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University of Michigan *

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100

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Mechanical Engineering

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Apr 3, 2024

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pdf

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2

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Engr 100 Section 450 W’16 Name: ___________________________________ Homework: Electricity (30pts) Lab section: Thu PM Fri AM Fri PM Due start of lecture Tu 16 Feb 2016 Show your work; attach if necessary. Significant figures count. You may consult your notes, resources in the library, or on the internet. [Note from 2020: the notation has been updated from that used back in 2016]. In Figure 1 below, the dashed box surrounds a stepper motor acting as a generator, V emf = K e f e , where f e is the electrical frequency, K e =0.0533 V/Hz, and V emf is the electromotive force. V emf , and all AC quantities, are expressed as an rms voltage unless stated otherwise. Unless requested to do otherwise, express AC voltages and currents as rms voltages and currents. R coil is not necessarily the same in each of the problems below. The voltmeter, when present, has a resistance, R vm , of 1.0M Ω (one megaohm). Figure 1. A circuit composed of a stepper motor (inside the dashed box), a resistive load R load and a resistive voltmeter, R vm , which monitors an rms voltage at the terminals of the stepper motor, denoted V term . The voltmeter also monitors the electrical frequency, f e . 1. (5 pts) What is the magnitude of the current through the stepper motor when f e =544Hz, V term =28.05V, R load =174.1 Ω and R vm is open? 2. (5 pts) Write down an expression for the instantaneous voltage across R load when f e =544Hz, V term =28.05V, R load =174 .1 Ω and R vm is open (ie. no voltmeter involved). V emf
3. (5 pts) When R load is 4000 Ω, 1%, what is the equivalent resistance of the load in parallel with the voltmeter? 4. (5 pts) What is the time-averaged power delivered to the load when f e =336Hz, V term =16.33V and R load = 60.9 Ω? 5. (5 pts) What is the electrical efficiency when f e =336Hz, V term =16.33V, R load = 60.9 Ω and R vm is open? 6. (5 pts) What is R coil when f e =137Hz, V term =6.83V, R load = 8 5 Ω and R vm is open?
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