Consider an ordinary 100w incandescent light bulb and a led light bulb that produces the same amount of light, but consumes 20w of electricity. assuming the values for purchase price and lifetime for each bulb, and a cost of electricity as given below, compute the number of hours of usage required for the led light bulb to become more cost-effective than the incandescent bulb for each case below. if the crossover in cost occurs because a new bulb must be purchased, you may take the number of hours to be equal to the time at which the bulb must be purchased. note: one year of moderate usage corresponds to ~1000 hours.

Assuming the the values for purchase price and lifetime for each bulb, and a cost of electricity are:

Incandescent Bulb

Power:100W

Purchase Price: $1.50

Lifetime:

Electricity cost: $0.10/kWh

LED Bulb

Power:20W

Purchase Price: $40

Lifetime:

Electricity cost: $0.10/kWh

Let's begin with the calculations:

The electric energy used for a bulb is:

(1)

Where is the electric power and the time the bulb is used.

And the operating cost is:

(2)

Where is the Electricity cost in units of

For the Incandescent Bulb:

(3)

(4) This is the electric energy used

Calculating the cost:

(5)

(6)

(7) This is the electricity cost for incandescent light bulb for 1000 hours

For the LED Bulb:

(8)

(9) This is the electric energy used by the LED bulb

Calculating the cost:

(10)

(11)

(12) This is the electricity cost for LED bulb for 25000 hours

As we can see the use of LED bulb for 25 years (25000 h) is $50, this means in 1 year the cost would be $2.

On the other hand, the use of Incandescent bulb for 1 year (1000 h) is $10.

This means using the LED bulb will result more cost-effective than the Incandescent bulb, although the initial investment is high.