How Is Percentage Uncertainty Calculated in Power Dissipation?

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To calculate the percentage uncertainty in power dissipation for a resistor with a current of 2.5 ± 0.05 mA and a resistance of 4.7 Ω ± 2%, the percentage errors from both measurements must be combined. The current's percentage uncertainty is derived from its absolute uncertainty, while the resistance's percentage uncertainty is given directly. When calculating power using the formula P = I²R, the total percentage uncertainty is found by adding the individual percentage uncertainties from the current and resistance. This approach is similar to calculating the area of a rectangle, where uncertainties are summed when multiplying dimensions. The final result will provide the percentage uncertainty in the power dissipation value.
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Homework Statement



In a simple electrical circuit, the current in a resistor is measured as 2.5 ± 0.05 mA. The resistor is marked as having a value of 4.7 Ω ± 2%. If these values were used to calculate the power dissipated in the resistor, what would be the percentage uncertainty in the value obtained?

Homework Equations



none

The Attempt at a Solution


please help me, what is the solution for this one? thanks

i'm sorry, i post this in the advanced physics too, I'm confused where to post this.. hope you can help me...
 
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moimoi24 said:

Homework Statement



In a simple electrical circuit, the current in a resistor is measured as 2.5 ± 0.05 mA. The resistor is marked as having a value of 4.7 Ω ± 2%. If these values were used to calculate the power dissipated in the resistor, what would be the percentage uncertainty in the value obtained?

Homework Equations



none

The Attempt at a Solution


please help me, what is the solution for this one? thanks

i'm sorry, i post this in the advanced physics too, I'm confused where to post this.. hope you can help me...

I think that when multiplying two quantities, you merely add the percentage errors??

In this case you are multiplying 3 things I x I x R as in P = I2R; so you would add all three percentage errors.
You are given the percentage error in R, and can calculate the percentage error in I from the values given.

Peter
 
Can you show me the solution? I'm confused... thanks peter...
 
moimoi24 said:
Can you show me the solution? I'm confused... thanks peter...

If you wish to calculate the area of a rectangle with length 5.0 ±0.1 cm by 10.0 ± 0.1 cm, and give a percentage uncertainty, then

A = l x w so Area = 50 cm2

Now the percentage error.
5.0 ± 0.1 means an uncertainty of 0.1 in 5 or 1 in 50 or 2%
10.0 ± 0.1 mans an uncertainty of 1 in 100 or 1%

SO the uncertainty in the answer is 3% [add them together]

So Area is 50 cm2 ± 3%

That is as close to the solution you seek I will give,
 
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