Chapter 26 AC Electricity
Friday, January 14, 2011
10:03 AM
Recall from high school that sine and cosine curves have the
same basic shape, they are just shifted relative to one-another.
Sine and cosine functions are collectively called "sinusoids" or
"sinusoidal functions." For a reminder of how to sketch such
the graphs of such functions, see
http://www.math.washington.edu/~m124/source/supps/week1/sinusoidal/sinusoidal.pdf
Sinusoidal functions have the form
y = A cos(kt c) + d
or
y = A sin(kt c) + d
where A is the amplitude, c/k is the phase shift, 2 /k is the
period (or wavelength), and d is the vertical shift.
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CQ 1 Identical resistors are connected to separate 12 V
AC sources. One source operates at 60 Hz, the other at 120
Hz. In which circuit, if either, does the resistor dissipate the
greater average power?
CQ 3 Lightbulbs in AC circuits "flicker" in intensity, though
the flickering is too fast for your eyes to sense it. If a light
bulb is connected to a 120 V/60 Hz power supply, how many
times a second does the bulb reach peak brightness?
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CP 3 A resistor dissipates 2.00 W when the rms voltage of
the emf is 10.0 V. At what rms voltage will the resistor
dissipate 10.0 W?
CP 5 A toaster oven is rated at 1600 W for operation at 120
V/60 Hz. (a) What is the resistance of the oven heater
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V/60 Hz. (a) What is the resistance of the oven heater
element? (b) What is the peak current through it? (c) What is
the peak power dissipated by the oven?
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CP 11 A power pack charging a cell phone battery has an
output of 0.40 A at 5.2 V (both rms). Determine the rms
current at the 120 V/60 Hz wall outlet where the power pack
is plugged in.
CP 13 The "power cube" transformer for a portable CD
player has an output of 4.5 V and 600 mA (both rms) when
plugged into a 120 V/60 Hz outlet. (a) If the primary coil has
400 turns of wire, how many turns are on the secondary
coil? (b) What is the peak current in the primary coil?
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CP 53 A 15-km-long, 230 kV aluminum transmission line
delivers 34 MW to a city. If we assume a solid cylindrical cable,
what minimum diameter is needed if the voltage decrease
along this run is to be no more than 1.0% of the transmission
voltage? The resistivity of aluminum is 2.7 × 10-8 Ω m.
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CP 15 A typical North American family uses 1000 kWh of
electricity per month. (a) Determine the average rms current
in the 120 V power line to the house. (b) On average, what is
the resistance of the active circuits in a household?
CP 17 The following appliances are connected to a single 120
V, 15 A circuit in a kitchen: a 330 W blender, a 1000 W coffee
pot, a 150 W coffee grinder, and a 750 W microwave oven. If
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pot, a 150 W coffee grinder, and a 750 W microwave oven. If
these are all turned on at the same time, will they trip the
circuit breaker?
CP 19 Suppose you leave a 110 W television and two 100 W
lightbulbs on in your house to scare off burglars while you go
out dancing. If the cost of electric energy in your town is
$0.12/kWh and you stay out for 4.0 hours, how much does
this robbery-prevention measure cost?
also see http://amasci.com/amateur/whygnd.html
CP 21 If you touch the terminal of a battery, the small
area of contact means that the skin resistance will be
relatively large; 50 kΩ is a reasonable value. What current
will pass through your body if you touch the two terminals
of a 9.0 V battery with your two hands? Will you feel it?
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Will it be dangerous?
CP 25 A bird is perched on a high-voltage transmission
wire. The transmission wire is 100 km long, has a resistance
of 7.0 Ω, and carries a current of 200 A. If the bird's feet
are 2.0 cm apart, what is the potential difference
between the bird's feet?
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