Question

Fluorescent lamps with resistances that can be adjusted from 80.0 Ωto
400.0 Ω are being produced. If such a lamp is connected to a 110 V emf
source, how much will it cost to operate the lamp at its maximum rated
power for 24 h? The cost of energy is $0.086/kW•h.

Answer 1

Ok. We need to find the maximum kW-hr this bulb. We already know the time, 24 hours. We just need the power of the bulb at maximum power.

Answer 2

Do you know the equation for power?

Answer 3

\[p=(\Delta V)^{2} / r\]

Answer 4

There ya go. So, which resistance will give us the maximum power of the bulb?

Answer 5

the 400 ohms

Answer 6

Try again.
P = V^2/R; P and R are inversely proportional. This means as R decreases or increases, P increases or decreases.

Answer 7

so then if we want P to be the highest we choose the lowest?

Answer 8

Right. If we want maximum power, we'll have to choose the lowest resistance possible, in this case, 80 Ohms. Do the math and figure out how many Watts we get.

Answer 9

we take the voltage which is 110 and square it and divide by the 80 ohm resistor?

Answer 10

Right. That gives us power in watts, not kilowatts.

Answer 11

so i change the watts into kilowatts and then i do all the math

Answer 12

thats a really small number though is that normal?

Answer 13

Well, when you find the power in watts. Convert it to kilowatts. Then find how many kW-hr that is for 24 hours.

Answer 14

For kilowatts? It should be, since it's a bigger unit.

Answer 15

ohh never mind haha
k thank
ill be back

Answer 16

it got that it came out to .15125 which should round with two significant figures to .15

Answer 17

I wouldn't round just yet. I would only round when it comes to the final answer.

Answer 18

alright

Answer 19

then i take the equation\[PA= p \Delta t (v)\]
where PA is the total amount of money, p is the power and t the time.... what is v?

Answer 20

Err...I'm not sure. Maybe it's just the cost of the kW-hr. Intuitively, you can see the cost is in units dollar per kW-hr. So we know we'll have to multiply the cost by how many kW-hrs we have.

Answer 21

ok
so its the time multiplied by the unit cost and the power to get the total

Answer 22

Yes, to get the total cost of the energy.

Answer 23

should the total cost of the energy be a small number? because it is

Answer 24

Should be lol. The cost per kWh is 8 cents.

Answer 25

That's, like, usual in real life as well. At least this is a real world problem.

Answer 26

alright well i got $0.2904

Answer 27

Whoa, that's not right.

Answer 28

exactly

Answer 29

Maybe it is. It is only one device, and it's only on for 24 hours in this problem. I can believe it. Is your problem multiple choice?

Answer 30

no
none of them are haha and i have alot

Answer 31

well i multiplied the power by the 24 hours and the per hour cost so it should be correct

Answer 32

I would believe so.

Answer 33

thanks

Answer 34

For the record I got 31.2 cents.

Answer 35

Math errors errwhere. She got close, 29 cents.

Answer 36

I'm also getting 31.2 cents lol.

Answer 37

i fixed it its because i was looking at the previous question and used .080 instead of .086