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Phet explorations: generator

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Generator

Section summary

  • Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
  • The voltage source of an alternating current (AC) system puts out V = V 0 sin 2 π ft size 12{V = V rSub { size 8{0} } "sin2"π ital "ft"} {} , where V size 12{V} {} is the voltage at time t size 12{t} {} , V 0 size 12{V rSub { size 8{0} } } {} is the peak voltage, and f size 12{f} {} is the frequency in hertz.
  • In a simple circuit, I = V/R size 12{I = ital "V/R"} {} and AC current is I = I 0 sin 2 π ft size 12{I = I rSub { size 8{0} } "sin2"π ital "ft"} {} , where I size 12{I} {} is the current at time t size 12{t} {} , and I 0 = V 0 /R size 12{I rSub { size 8{0} } = V rSub { size 8{0} } ital "/R"} {} is the peak current.
  • The average AC power is P ave = 1 2 I 0 V 0 size 12{P rSub { size 8{"ave"} } = { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } } {} .
  • Average (rms) current I rms size 12{I rSub { size 8{"rms"} } } {} and average (rms) voltage V rms size 12{V rSub { size 8{"rms"} } } {} are I rms = I 0 2 size 12{I rSub { size 8{"rms"} } = { {I rSub { size 8{0} } } over { sqrt {2} } } } {} and V rms = V 0 2 size 12{V rSub { size 8{"rms"} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {} , where rms stands for root mean square.
  • Thus, P ave = I rms V rms size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {} .
  • Ohm’s law for AC is I rms = V rms R size 12{I rSub { size 8{"rms"} } = { {V rSub { size 8{"rms"} } } over {R} } } {} .
  • Expressions for the average power of an AC circuit are P ave = I rms V rms , P ave = V rms 2 R , and P ave = I rms 2 R , analogous to the expressions for DC circuits.

Conceptual questions

Give an example of a use of AC power other than in the household. Similarly, give an example of a use of DC power other than that supplied by batteries.

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Why do voltage, current, and power go through zero 120 times per second for 60-Hz AC electricity?

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You are riding in a train, gazing into the distance through its window. As close objects streak by, you notice that the nearby fluorescent lights make dashed streaks. Explain.

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Problem exercises

(a) What is the hot resistance of a 25-W light bulb that runs on 120-V AC? (b) If the bulb’s operating temperature is 2700º C , what is its resistance at 2600º C ?

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Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?

480 V

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A certain circuit breaker trips when the rms current is 15.0 A. What is the corresponding peak current?

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Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

2.50 ms

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A North American tourist takes his 25.0-W, 120-V AC razor to Europe, finds a special adapter, and plugs it into 240 V AC. Assuming constant resistance, what power does the razor consume as it is ruined?

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In this problem, you will verify statements made at the end of the power losses for [link] . (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a 1 . 00 - Ω size 12{1 "." "00"- %OMEGA } {} transmission line. (c) What percent loss does this represent?

(a) 4.00 kA

(b) 16.0 MW

(c) 16.0%

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A small office-building air conditioner operates on 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs 9.00 cents /kW h size 12{9 "." "00"" cents/kw" cdot h} {} ?

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What is the peak power consumption of a 120-V AC microwave oven that draws 10.0 A?

2.40 kW

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What is the peak current through a 500-W room heater that operates on 120-V AC power?

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Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

(a) 4.0

(b) 0.50

(c) 4.0

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Nichrome wire is used in some radiative heaters. (a) Find the resistance needed if the average power output is to be 1.00 kW utilizing 120-V AC. (b) What length of Nichrome wire, having a cross-sectional area of 5.00 mm 2 size 12{5 "." "00"" mm" rSup { size 8{2} } } {} , is needed if the operating temperature is 500º C size 12{"500"°C} {} ? (c) What power will it draw when first switched on?

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Find the time after t = 0 size 12{t=0} {} when the instantaneous voltage of 60-Hz AC first reaches the following values: (a) V 0 / 2 size 12{V rSub { size 8{0} } /2} {} (b) V 0 size 12{V rSub { size 8{0} } } {} (c) 0.

(a) 1.39 ms

(b) 4.17 ms

(c) 8.33 ms

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(a) At what two times in the first period following t = 0 size 12{t=0} {} does the instantaneous voltage in 60-Hz AC equal V rms size 12{V rSub { size 8{"rms"} } } {} ? (b) V rms size 12{-V rSub { size 8{"rms"} } } {} ?

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Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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