Question

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

Answer 1

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`

Step-by-step 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 = (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  =  (t_3)/( t)`

=>
`N  =  (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 =  (t_3)/( t_k)`

=>
`M  =  (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 =  (V^2)/(P)`

`R  =  (120^2)/(23)`

`R =  626.1 \Omega`