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20.4 Electric power and energy  (Page 4/7)

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Making connections: take-home experiment—electrical energy use inventory

1) Make a list of the power ratings on a range of appliances in your home or room. Explain why something like a toaster has a higher rating than a digital clock. Estimate the energy consumed by these appliances in an average day (by estimating their time of use). Some appliances might only state the operating current. If the household voltage is 120 V, then use P = IV size 12{P = ital "IV"} {} . 2) Check out the total wattage used in the rest rooms of your school's floor or building. (You might need to assume the long fluorescent lights in use are rated at 32 W.) Suppose that the building was closed all weekend and that these lights were left on from 6 p.m. Friday until 8 a.m. Monday. What would this oversight cost? How about for an entire year of weekends?

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The illustration shows a circuit drawn in a rectangle with a long and short parallel on the left and jagged line resistor labeled R on the right side. To the right of the circuit diagram is a graph with and arrow pointing up on the y axis and labeled E. The horizontal axis is represented by an arrow pointing to the right and labeled t. There is a straight diagonal line originating a the origin labeled 0 and ending at t1 on the x-axis (indicated with a dotted line going from t1 to the tip of the line) and E1 on the y-axis (also indicated with a dotted line).

The circuit shown contains a resistor R connected to a voltage supply. The graph shows the total energy E dissipated by the resistance as a function of time. Which of the following shows the corresponding graph for double resistance, i.e., if R is replaced by 2 R ?

  1. There are four graphs with the same x-axis (t) and y-axis (E) shown in figure Ch20S05. All four graphs have straight, diagonal lines ending at t1 (with a dotted line) on the x-axis. The slopes of the line vary; however because they end at different values on the y-axis. Graph A has the steepest slope and the y-ending value for the line is 2E1. Graph B has the second steepest slope and the y-ending value is E1. Graph C's slope is less steep still and ends at E1 over 2. Graph D has the flattest slop and ends at E1 over 4.
  2. There are four graphs with the same x-axis (t) and y-axis (E) shown in figure Ch20S05. All four graphs have straight, diagonal lines ending at t1 (with a dotted line) on the x-axis. The slopes of the line vary; however because they end at different values on the y-axis. Graph A has the steepest slope and the y-ending value for the line is 2E1. Graph B has the second steepest slope and the y-ending value is E1. Graph C's slope is less steep still and ends at E1 over 2. Graph D has the flattest slop and ends at E1 over 4.
  3. There are four graphs with the same x-axis (t) and y-axis (E) shown in figure Ch20S05. All four graphs have straight, diagonal lines ending at t1 (with a dotted line) on the x-axis. The slopes of the line vary; however because they end at different values on the y-axis. Graph A has the steepest slope and the y-ending value for the line is 2E1. Graph B has the second steepest slope and the y-ending value is E1. Graph C's slope is less steep still and ends at E1 over 2. Graph D has the flattest slop and ends at E1 over 4.
  4. There are four graphs with the same x-axis (t) and y-axis (E) shown in figure Ch20S05. All four graphs have straight, diagonal lines ending at t1 (with a dotted line) on the x-axis. The slopes of the line vary; however because they end at different values on the y-axis. Graph A has the steepest slope and the y-ending value for the line is 2E1. Graph B has the second steepest slope and the y-ending value is E1. Graph C's slope is less steep still and ends at E1 over 2. Graph D has the flattest slop and ends at E1 over 4.
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What will be the ratio of the resistance of a 120 W, 220 V lamp to that of a 100 W, 110 V lamp?

10:3 or 3.33

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Section summary

  • Electric power P size 12{P} {} is the rate (in watts) that energy is supplied by a source or dissipated by a device.
  • Three expressions for electrical power are
    P = IV, size 12{P = ital "IV,"} {}
    P = V 2 R , size 12{P = { {V rSup { size 8{2} } } over {R} } ","} {}

    and

    P = I 2 R . size 12{P = I rSup { size 8{2} } R"."} {}
  • The energy used by a device with a power P size 12{P} {} over a time t size 12{t} {} is E = Pt size 12{E = ital "Pt"} {} .

Conceptual questions

Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?

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The power dissipated in a resistor is given by P = V 2 / R size 12{P = V rSup { size 8{2} } /R} {} , which means power decreases if resistance increases. Yet this power is also given by P = I 2 R size 12{P = I rSup { size 8{2} } R} {} , which means power increases if resistance increases. Explain why there is no contradiction here.

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Problem exercises

What is the power of a 1.00 × 10 2 MV lightning bolt having a current of 2.00 × 10 4 A ?

2 . 00 × 10 12 W size 12{2 "." "00"´"10" rSup { size 8{"12"} } " W"} {}

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What power is supplied to the starter motor of a large truck that draws 250 A of current from a 24.0-V battery hookup?

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A charge of 4.00 C of charge passes through a pocket calculator's solar cells in 4.00 h. What is the power output, given the calculator's voltage output is 3.00 V? (See [link] .)

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Photograph of a small calculator having a strip of solar cells just above the keys.
The strip of solar cells just above the keys of this calculator convert light to electricity to supply its energy needs. (credit: Evan-Amos, Wikimedia Commons)

How many watts does a flashlight that has 6.00 × 10 2 C pass through it in 0.500 h use if its voltage is 3.00 V?

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Find the power dissipated in each of these extension cords: (a) an extension cord having a 0 . 0600 - Ω size 12{0 "." "0600-" %OMEGA } {} resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of 0 . 300 Ω . size 12{0 "." "300" %OMEGA } {}

(a) 1.50 W

(b) 7.50 W

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Verify that the units of a volt-ampere are watts, as implied by the equation P = IV size 12{P = ital "IV"} {} .

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Show that the units 1 V 2 / Ω = 1 W size 12{1" V" rSup { size 8{2} } / %OMEGA =1" W"} {} , as implied by the equation P = V 2 / R size 12{P = V rSup { size 8{2} } /R} {} .

V 2 Ω = V 2 V/A = AV = C s J C = J s = 1 W

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Show that the units 1 A 2 ⋅ Ω = 1 W size 12{1" V" rSup { size 8{2} } / %OMEGA =1" W"} {} , as implied by the equation P = I 2 R size 12{P = I rSup { size 8{2} } R} {} .

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Verify the energy unit equivalence that 1 kW ⋅ h = 3 . 60 × 10 6 J size 12{1" kW" cdot "h = 3" "." "60"´"10" rSup { size 8{6} } " J"} {} .

1 kW ⋅ h= 1 × 10 3 J 1 s 1 h 3600 s 1 h = 3 . 60 × 10 6 J size 12{1" kW" cdot "h=" left ( { {1 times "10" rSup { size 8{3} } " J"} over {"1 s"} } right ) left (1" h" right ) left ( { {"3600"" s"} over {"1 h"} } right )=3 "." "60" times "10" rSup { size 8{6} } " J"} {}

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Questions & Answers

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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