Mean power dissipated in resistor in ac circuit

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Homework Help Overview

The discussion revolves around calculating the mean power dissipated in a resistor within an AC circuit context. The original poster expresses confusion regarding the application of concepts related to AC circuits, particularly in relation to averaging current values.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the average current by simply adding values and dividing, leading to uncertainty about the correct approach to calculating power. Some participants suggest considering the relationship between power and the square of the current, raising questions about why squaring the average current is not appropriate.

Discussion Status

Participants are exploring the mathematical principles behind power calculations in AC circuits. There is a focus on clarifying the distinction between the mean of the squares and the square of the mean, with some guidance provided on the correct approach to determining mean power.

Contextual Notes

The original poster indicates a lack of prior knowledge in AC circuits, which may affect their understanding of the problem. There is an emphasis on the need to grasp the underlying principles of power calculations in this context.

toforfiltum
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Homework Statement


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Homework Equations

The Attempt at a Solution


I am surprised that this question came up, I haven't learned ac circuits yet. I don't know how to solve this. I just added both values and current and divide it by two, which gives me 1.5A, since I thought it's the average but I'm wrong. Answer is C. I really don't know how to get that value.
 
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The reason your method didn't work is due to the fact that the power is not proportional to the current. It's proportional to the square of the current.

It might help to determine the value of the power when the current is 2 A and the value when the current is -1 A.
 
TSny said:
The reason your method didn't work is due to the fact that the power is not proportional to the current. It's proportional to the square of the current.

It might help to determine the value of the power when the current is 2 A and the value when the current is -1 A.
Oh I see. Thanks. I have to do it this way because power is a scalar, is it? Why can't I square the value of 1.5A instead?
 
toforfiltum said:
Oh I see. Thanks. I have to do it this way because power is a scalar, is it?
It's not because its a scalar quantity, it's because the mean of the square of a quantity is not equal to the square of the mean of the quantity. For example, for the two numbers 2 and 4 the mean of the square of the numbers is (22 + 42)/2 = 10. But the square of the mean of the numbers is 32 = 9.

Power is proportional to the square of the current. So you need to use the mean of the square of the current to get the mean power.
 
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TSny said:
It's not because its a scalar quantity, it's because the mean of the square of a quantity is not equal to the square of the mean of the quantity. For example, for the two numbers 2 and 4 the mean of the square of the numbers is (22 + 42)/2 = 10. But the square of the mean of the numbers is 32 = 9.

Power is proportional to the square of the current. So you need to use the mean of the square of the current to get the mean power.
Thanks for the really neat explanation.
 

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