Power dissipation by resistor Q. TBR

[gwjib04]

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From TBR book section 9

Example 9.1b
For a fixed potential difference across a resistive wire, the power drain through the resistor can be increased by increasing the:

B. length of the wire
D. conductivity of the wire

This must be a "BEST" answer scenario but I can't see how one is better than the other.

Conductivity increases current therefore, more current, more drift = more energy lost.
But length of wire would also increase the resistance because the wire is a source of resistance...maybe I should be ignoring the inherent resistance of the wire?

 

[Postictal Raiden]

From TBR book section 9

Example 9.1b
For a fixed potential difference across a resistive wire, the power drain through the resistor can be increased by increasing the:

B. length of the wire
D. conductivity of the wire

This must be a "BEST" answer scenario but I can't see how one is better than the other.

Conductivity increases current therefore, more current, more drift = more energy lost.
But length of wire would also increase the resistance because the wire is a source of resistance...maybe I should be ignoring the inherent resistance of the wire?

Power = (I^2)R. Increasing the current by factor of x, increases the power drain by factor of x^2. On the other hand, increasing R will increase power drain by only one factor.

 

[BerkReviewTeach]

More energy lost = more energy lost per time = more power drain.

The equation you need is P = I²R.

If conductivity goes up, then the wire has more current and less resistance, resulting in a larger P drain.

 

[milski]

It maybe easier to use the equivalent equation, P=V²/R. You can see from it how for a constant V, increasing R actually decreases the power.

Keep in mind that the two answers are opposite to each other - increasing the length is the same as increasing the resistance, increasing the conductivity is the same as decreasing the resistance. It's not a matter of best or not, it's a wrong vs right.

 

[gwjib04]

Ibn,
Thanks for pointing out current increases power dissipation with its square.

I should have noticed that they want to increase power dissipated through the resistor not simply increased power (lost by the whole system). If you increased the length, resistance would increase and you'd lose more power but it wouldn't be through the resistor.

Keep in mind that the two answers are opposite to each other - increasing the length is the same as increasing the resistance, increasing the conductivity is the same as decreasing the resistance.

Milski, I think increased length and increased conductivity have opposite effects on resistance but their effects on power are the same. So I still think its a best answer question

By the way, what's the rule for applying the 2 different power equations? Isn't one just for Ohmic devices?

 

[milski]

Ibn,
Thanks for pointing out current increases power dissipation with its square.

I should have noticed that they want to increase power dissipated through the resistor not simply increased power (lost by the whole system). If you increased the length, resistance would increase and you'd lose more power but it wouldn't be through the resistor.



Milski, I think increased length and increased conductivity have opposite effects on resistance but their effects on power are the same. So I still think its a best answer question

By the way, what's the rule for applying the 2 different power equations? Isn't one just for Ohmic devices?

Length does not affect power directly - it only changes the resistance which in turn changes power. Power depends on potential and resistance, why would the reason for the change in the resistance matter?

All three formulas are equivalent and applicable for ohmic device (resistors only). You can use whichever is easier. When you need to compare the result of some change it's useful to use a formula which has only one variable changing, like V²/R, instead I²R, where both I and R change simultaneously and the total change is harder to quantify without knowing more.

 

[BerkReviewTeach]

Ibn,
I think increased length and increased conductivity have opposite effects on resistance but their effects on power are the same. So I still think its a best answer question

You are right that increasing the length of the resistor has the oppoisite effect of increased conductivity (which is reduced resistance). But the problem here is that you are only considering the impact of resistance on power when you are thinking about the length. Because V is constant, a longer resistor not only raises resistance, but it also lowers current (by the same factor). So again, it helps to look at P = I²R. A longer resistor will reduced the power, because a decrease in I when squared is more significant than the increase in resistance.