Calculate Power Consumption: 600W Device at 220V to 160V | 1W Precision

[chawki]

Homework Statement

An electrical device consumes 600 W of power, when connected to 220 V voltage.

Homework Equations

Calculate the power consumption of the device, when it is connected in 160 V voltage. Give the answer in 1 W precision.

The Attempt at a Solution

I tried and found I=2.72 amps, R=80.88 Ohms, and W=316.51

 

[Dadface]

Looks good.You need to round up the final answer and for problems of this type it's probably best to do the rounding up at the end.

 

[tiny-tim]

hi chawki!

I tried and found I=2.72 amps, R=80.88 Ohms, and W=316.51

yeees …

but now do it the quick way (ie, without bothering to find I or R) …

when you vary V, what is Q proportional to?

 

[chawki]

Oh please Tiny-Tim...don't tease me on this one too

 

[chawki]

317?

 

[tiny-tim]

write out all the equations (for W V I and R) …

eliminate I (since you don't know what I is), that should give you just W V and R …

then assume that R is constant …

how does W depend on V ?

 

[chawki]

W=V^2 / R
But what does it have to do if it is proportional to V^2

 

[tiny-tim]

if W = V²/R

and if V is decreased from 220 to 160 (and R stays the same) …

how much is W increased? ​

 

[chawki]

i give up

 

[chawki]

To Dadface...
Is it 317watts ?

 

[chawki]

It is said to give the answer in 1watt precision

 

[chawki]

since there is .51 the answer would be 317watts?

 

[ehild]

Yes. And even more so if you do not make that rounding error in the current.

ehild

 

[chawki]

We need to round also the current??
They asked only the answer to be rounded...

 

[ehild]

You rounded it to 2.72. It is wrong. It was 600/220=2.727272~2.727 A. The resistance is 220/2.727=80.67 ohm.

You should use at least one more significant digits in the intermediate results than in the final result.

ehild