Question

An electric bulb is rated 220 V and 100 W. When it is operated on 110 V.Find the POWER.

Answer 1

Well, power is directly proportional to voltage?

Answer 2

yeah. I know it very well

Answer 3

Well, I don't... I'm not even sure of that ^
:D
Sorry~

Answer 4

\[\huge P~ ~~\alpha ~~~~V ~and~ I\]

Answer 5

Well, actually,
\[\Large P \propto V\] if current is constant, but it may well not be... what might be constant is the resistance, in which case, given...
\[\Large P = \frac{V^2}R\]\[\Large \color{blue}{P\propto V^2}\]instead...

Answer 6

@terenzreignz why we use \(\large \frac{V^2}{R}\) ?
Why don't we use only \(\large VI\)??

Answer 7

any reason behind it ? @terenzreignz

Answer 8

Because we know it's the same lightbulb, and therefore, the same resistance.

Answer 9

but current is also the same in both the bulbs

Answer 10

@Diwakar help me

Answer 11

what is the confusion? @terenzreignz has showed how to solve it above. Power is proportional to the square of voltage. So, when u halve the voltage power becomes one-fourth.

Answer 12

@Diwakar why can't we use \(\large VI\) formula ?

Answer 13

tell me @Diwakar

Answer 14

We are using this formula ,although implicitly. You see I=V/R. So, put this in your formula and see that you are getting P=V\(^{2}\)/R

Answer 15

@Diwakar you use V^2/R formula. Why we can't use VI formula. It also finds the power.
That's was my real problem

Answer 16

these 2 formulas are same (at least in this problem). Look:
P=VI =V *(V/R) =V^2/R

Answer 17

the advantage of using this form is that R is constant no matter whether you are applying 220 or 110.

Answer 18

when we use VI formula, the power is 50 W and when we use V^2/R formula, the power is 25 W.
What will be correct answer?

Answer 19

How are you getting 50W ?
Let us see.First find resistance of bulb.

As,P=V^2/R
When you put V=220 and P=100. We get R=484 ohms.

Now, let us find current when 110 V is applied
I=V/R=110/484

P=VI=(110*110)/484 =\(\color{red}{25W}\)

Answer 20

thank you :) for helping me.. @Diwakar

Answer 21

no problem!

Answer 22

@Diwakar sorry for disturbing you...

so tell me that 50 W is wrong answer?

Answer 23

25 is correct. 50 is wrong.

Answer 24

thank you :)