Charge entering and leaving a light bulb

[iriver4]

Homework Statement

A light bulb is rated at 30 w when operated at 120 v. How much charge enters (and leaves) the light bulb in 4.0 min?

ans is 17 C

Homework Equations

I = P/V
i = dq/dt

The Attempt at a Solution

I = P/V = 30/120 = 0.25A

q = I*t = (0.25)(4*60) = 60 C

thinking maybe the answer given is a typo but need confirmation please

 

[berkeman]

Homework Statement

A light bulb is rated at 30 w when operated at 120 v. How much charge enters (and leaves) the light bulb in 4.0 min?

ans is 17 C

Homework Equations

I = P/V
i = dq/dt

The Attempt at a Solution

I = P/V = 30/120 = 0.25A

q = I*t = (0.25)(4*60) = 60 C

thinking maybe the answer given is a typo but need confirmation please

Interesting. Your answer looks correct.

I thought a bit about if the difference could be that the 0.25A is RMS, and maybe there needs to be some correction for that. But the RMS value is what is used in the power calculation, and is equivalent to the DC value that the current would have if the light bulb were run on DC instead of AC.

Does anybody else see where the 17C came from?

 

[CWatters]

I agree with 60C.

Google found 17C was one of the other multi choice answers when the question was slightly different. See here..

http://www.chegg.com/homework-help/questions-and-answers/thank-ur-help-light-bulb-rated-30-w-whenoperated-120-v-charge-enters-leaves-lightbulb-10-m-q200233

 

[rude man]

Maybe it's my daily allotment of Shiraz, but my vote is zero:
q = integral i dt = 0 over 4*60*60 integer cycles.

 

[haruspex]

Maybe it's my daily allotment of Shiraz, but my vote is zero:
q = integral i dt = 0 over 4*60*60 integer cycles.

You raise the key question of whether this is DC or AC. However, even if it is AC we can get a nonzero result by noting that it doesn't matter which way the charge flows in at any time, so it's ∫|I|.dt. OTOH, this gives me 2PT/(πV) = 2*30*240/(π*120) ≈ 38C.

 

[rude man]

You raise the key question of whether this is DC or AC. However, even if it is AC we can get a nonzero result by noting that it doesn't matter which way the charge flows in at any time, so it's ∫|I|.dt. OTOH, this gives me 2PT/(πV) = 2*30*240/(π*120) ≈ 38C.

?
A semantic issue. I'll stick with zero C.

 

[mukundpa]

If it is an AC than the current calculated is rms current. Peak value of this current will be I_max = 0.25*√2 A

To calculate charge flowing in one direction only we have to integrate instantaneous current for half cycle and thus the average current for half cycle is 2 I_max/π.

In 4 min charge is flowing in one direction for 2 min and thus the net charge flow in one direction during 4 min (for 2 min) will be
(2√2*0.25/π)*2*60 = 27 C

 

[SammyS]

If it is an AC than the current calculated is rms current. Peak value of this current will be I_max = 0.25*√2 A

To calculate charge flowing in one direction only we have to integrate instantaneous current for half cycle and thus the average current for half cycle is 2 I_max/π.

In 4 min charge is flowing in one direction for 2 min and thus the net charge flow in one direction during 4 min (for 2 min) will be
(2√2*0.25/π)*2*60 = 27 C

I like it !