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aniked [119]
3 years ago
12

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost m

uch more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 W incandescent bulb uses only 23.0 W of power. The compact bulb lasts 10000 hours, on the average, and costs $ 12.00, whereas the incandescent bulb costs only $ 0.76, but lasts just 750 hours. The study assumed that electricity cost $ 0.090 per kilowatt-hour and that the bulbs were on for 4.0 h per day.
Required:
a. What is the total cost (including the price of the bulbs) to run each bulb for 3.0 years?
b. How much do you save over 3.0 years if you use a compact fluorescent bulb instead of an incandescent bulb?
c. What is the resistance of a "100-W" fluorescent bulb?
Physics
1 answer:
prohojiy [21]3 years ago
7 0

Answer:

a

The  \ price \  for \   Compact\ fluorescent\ bulbs \ is  \ C_T  = \$ 21.067\\The   \ price \  for \    incandescent\ bulb \ is \ C_t  = \$ 43.98

b

The \  amount  \  saved \ is  \ C_S =  \$ 22.913

c

The \ resistance \  is \ R =  626.1 \Omega

Explanation:

From the question we are told that

   The power used by incandescent bulb P_r  =  23.0 W

    The power used by  Compact fluorescent bulb P_p  =  100W

     The life span of  Compact fluorescent bulb is  t = 1000 \  hours

    The  prices of   Compact fluorescent bulb is C_c = \$ 12

    The  prices of incandescent bulb is C_i = \$ 0.76

     The life span of   incandescent bulb is  t_k = 750   \ hours

      The cost of electricity is C_e =  \$ 0.090/ kilowatt-hour = \frac{0.090}{1000} = \$0.00009 / W / h

    The duration of daily bulb usage is t_d  =  4 \  hours

     

Generally 3 years of bulb usage  in hours is mathematically evaluated as

    t_3 =  3 *  365 *  t_d

=>   t_3 =  3 *  365 *  4

=>   t_3 =  4380 \ h

Generally the cost to power a 23W bulb for the above duration  is mathematically represented as

 Z = 23 *  t_3 * C_e

=>   Z = 23 *  4380 * 0.00009

=>   Z = \$ 9.0667

The number of Compact fluorescent bulbs required to  achieve this about of time is mathematically represented as

       N  =  \frac{t_3}{ t}

=>  N  =  \frac{4380}{1000}

=>   N  = 0.438

=>  N  \approx  1

The total cost of  usage  for the Compact fluorescent bulb   is  mathematically represented as

      C_T  =  Z +C_c

=>   C_T  =  9.0667 +12

=>   C_T  = \$ 21.067    

The number of  incandescent bulbs required to  achieve this about of time is mathematically represented as

       M =  \frac{t_3}{ t_k}

=>  M  =  \frac{4380}{750}

=>   M  = 6

Generally the cost to power a 100W bulb for the above duration  is mathematically represented as

 Z = 100 *  t_3 * C_e

=>   Z = 100 *  4380 * 0.00009

=>   Z = \$ 39.42

The total cost of  usage  for the incandescent bulbs    is  mathematically represented as

      C_t  =  C_e + [6 *C_i]

=>   C_t  =  39.42 + [0.76 *  6]

=>   C_t  = \$ 43.98    

Generally the total amount saved is mathematically represented as

   C_S =  C_t - C_T

=>   C_S =  43.98 - 21.067

=>   C_S =  \$ 22.913

Generally the resistance of the Compact fluorescent bulb is  

    R =  \frac{V^2}{P}

    R  =  \frac{120^2}{23}

R =  626.1 \Omega

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