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Old May 5th 2016, 05:39 AM   #1
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power consumption

The question is

An electric bulb is rated 220 V and 100 W.
When it is operated on 110 V, the power consumed will be __________.

I proceed with P = VI.

I found I (electric current) = 100/220.

This I substituted in P = VI.

= 110 * (100/220) = 50.

But they say the answer is 25 W.

Where I went wrong?

Kindly enlighten me.

with thanks and regards,

Aranga
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Old May 5th 2016, 06:24 AM   #2
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You are assuming, incorrectly, that the current is the same in both cases. It's not.

Start by considering that the resistance of the incandescent bulb is a constant. You can calculate the value of the resistance from P_1 = V_1^2/R. Now that you have a value for R, you can use it to calculate a new value of power for a different voltage using P_2 = V_2^2/R. Alternatively you can divide the second equation by the first:

P_2/P_1 = (V_2^2)/(V_1^2)

From this you can see that if V_2 = (1/2) V_1, then P_2 = (1/4) P_1.

Another approach is to recognize from V=IR that if V is cut in half then I must be cut in half (assuming constant R). Then from P_2 = V_2 I_2 you have that both V_2 and I_2 are half their original values. Hence P_2 is 1/4 its original value.

Last edited by ChipB; May 9th 2016 at 07:17 AM.
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Old May 6th 2016, 12:15 AM   #3
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Sir,

Excellent. Now I understand. I always have the confusion when to use which. P=VI, P = (V^2)/R and P = (I^2)*R.

With Best wishes,

Aranga
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Old May 12th 2016, 01:31 AM   #4
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The wave formula that I would use is speed = wavelenght/period so 170/0,6 = 283
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