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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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