# kWh

Discussion in 'Homework Help' started by kbwelch17, Sep 14, 2013.

1. ### kbwelch17 Thread Starter New Member

Sep 14, 2013
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Hi all:

I am just starting Circuit Theory and am taking Physics 2 concurrently. As such, I am new to many of the subjects and terminology used in the book I am using and am finding reading it quite a challenge (For those interested, it is The Analysis & Design of Linear Circuits by Thomas/Rosa/Toussaint). Anyway I am having trouble figured out a particular problem on our first problem set:

1-14: An incandescent lamp absorbs 100 W when connected to a 120-V source. An energy-efficient compact fluorescent lamp (CFL) producing the same amount of light absorbs 16 W when connected to the same source. How much cheaper is it to operate the CFL versus the incandescent bulb over 1,000 hours when electricity costs 7.8 cents/kWh?

My main issue here I suppose is the concept of kWh. Is this kilowatts absorbed per hour? If that is the case, why does the voltage of the source matter? I am sure I will visit this page often throughout the semester!

Thanks.

Jul 18, 2013
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Watts are a product of Current and voltage.
Max.

3. ### WBahn Moderator

Mar 31, 2012
17,716
4,788
I think you've put yourself at a disadvantage by not taking Physic 2 first. It is almost always a prereq for a Circuits I course and with good reason.

The unit of the "watt" is power -- how much energy is absorbed, produced, transferred, processed, or whatever, per unit time. In SI units it is 1W=1J/s=1Nm/s

A kWh is (1kW)*(1hour). So if W is energy/time, the kWh is (energy/time)(time)=energy.

Specifically, (1000J/s)(3600s) = 3.6MJ.

The phrase "kilowatts absorbed per hour" is meaningless. Think of something comparable, like if there were a unit of mph-s (mile-per-hour-second). The mph is a rate (distance/time). If you multiply how fast you are going by a length of time, you just get a distance (in this case about 1.5ft). It would make no sense to speak of this as somehow being the speed gone per second.

As for the voltage -- why do you think it matters?

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4. ### kbwelch17 Thread Starter New Member

Sep 14, 2013
5
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Okay - first of all thank you for the quick response. I actually mentioned that to my adviser during registration last year and he told me it wouldn't be a problem, however it is immediately apparent that a lot of the material overlaps.

As far as the problem goes, I understand now that kWh is a unit of energy rather than a rate. In this case, the incandescent lamp absorbs 100 J/s of energy and thus over a 1,000 hour span will absorb 3.6X10^8 J. This is 100 kWh and thus costs \$7.80 per the above rate. Likewise, a device that absorbs 16 W when connected to a 120V source will cost \$1.25 over 1,000 hours by the same method. This saves the user \$6.55.

If this is correct (which I am not 100% sure it is). I still am unsure about the significance of the voltage. I understand I can find current through the relationship between voltage and power but I see no reason why current comes into play in this problem. The 120 V number seems arbitrary other than perhaps to confirm that the lamps were connected to the same source.

5. ### WBahn Moderator

Mar 31, 2012
17,716
4,788
The mentioning of the voltage is superfluous. In the "real world", you are going to have to determine what information is important and what is not, so many problems in your courses will include additional information so that you can develop that ability.

6. ### WBahn Moderator

Mar 31, 2012
17,716
4,788
BTW -- Your computations are correct.

7. ### kbwelch17 Thread Starter New Member

Sep 14, 2013
5
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I see. Thanks a lot for your help here!