# Wires with constant power and increasing voltage

• MathewsMD
In summary, the conversation discusses Ohm's Law and its application to materials with varying resistivity and resistance. It is clarified that Ohm's Law only shows a linear relationship between current and potential, and that R is constant for materials that follow Ohm's Law. The question then arises whether resistivity and resistance are constant for materials that do not follow Ohm's Law, and if heating in a wire depends on both resistance and current. The attached question assumes that the wire follows Ohm's Law, and the correct answer is circled while incorrect answers are discussed. The conversation also touches on the relationship between voltage and current, and how increasing one can affect the other. The conversation ends with a request for clarification on the different types of
MathewsMD
My question is in the attached image.
Before going right at it, I thought it would be best to clarify a few details.

Ohm's Law only shows that current and potential are linearly related, correct? So R is constant in the case of a material that follows Ohm's Law (metal conductors for the most part, right?). But regardless of the material, isn't resistivity and as a result resistance of an object w/ constant length and surface also a constant? Or does it vary with current/potential? Isn't V = IR the definition of resistance? Do all three variables change in no particular pattern for materials that do not follow Ohm's Law?

Also, does heating in a wire depend on BOTH resistance and current? Are there any other factors?

Now, to the attached question, I am assuming that the wire follows Ohm's Law (is that a reasonable assumption?). I've circled the correct answer, but cannot quite understand why C and E are wrong. We know P is constant, and so is R if it follows Ohm's Law (once again, would R be constant if the material did not obey Ohm's Law?). Thus b is false since resistance of the wires stays the same. And even if it did change, P = V2/R, so resistance would not decrease. Also, isn't insulation related to resistance? Assuming constant resistance, this property does not change, so d is wrong.

Now, I know P = IV, and if V increases then I decreases. But if V= IR and R is a constant, if V increases doesn't I increases as well? What am I missing here? Also, isn't the IR drop simple V (V=IR). If V increases, then doesn't IR as well?

Just so you know, we were told all answers but a are false. Any comments on why and could you possibly critique my reasoning as well? Thanks!

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Have you worked out what the current would be in the two different cases?

Yes, assume resistance does not change significantly with current or voltage, in cables.

NascentOxygen said:
Have you worked out what the current would be in the two different cases?

Yes, assume resistance does not change significantly with current or voltage, in cables.

We didn't really calculate much with this question in class, we just went over the choices with reasoning.

I understand that since P = constant = IV, that current would decrease in this case. I am assuming increased current (or resistance for other cases) increases heat production, which is why a would be right. By problem lies with why V = IR is not exactly telling us the same thing. I know current decreases with increasing voltage when power is constant as given by P = IV, but then is V/I = R and R is also a constant, how would increasing V decrease I? Also, isn't IR the same thing as potential, so as potential, V, increases s does the IR drop?

You are getting your V's confused. There is the V related to supply voltage, and there is the V related to losses in cable resistance.

NascentOxygen said:
You are getting your V's confused. There is the V related to supply voltage, and there is the V related to losses in cable resistance.

Hmmm...okay...do you mind expanding on this a bit or referring me to any sources you think are relevant? I kind of thought they were both the related...

Also, any answers for the other questions I posted?

## 1. What is the relationship between power and voltage in wires with constant power and increasing voltage?

The relationship between power and voltage in wires with constant power and increasing voltage is that as voltage increases, power also increases. This is because power is equal to the product of voltage and current, and in a wire with constant power, the current must also increase to maintain the constant power. Therefore, as voltage increases, current must also increase to maintain the same power, resulting in a direct relationship between the two.

## 2. How does the resistance of the wire affect the power and voltage in this scenario?

The resistance of the wire affects the power and voltage in this scenario by causing a decrease in voltage as the current increases. This is due to Ohm's Law, which states that voltage is equal to current multiplied by resistance. As the current increases, the resistance of the wire causes a drop in voltage, resulting in a decrease in power. Therefore, in a wire with constant power and increasing voltage, the resistance of the wire must be taken into account.

## 3. Is there a limit to how much the voltage can increase in a wire with constant power?

Yes, there is a limit to how much the voltage can increase in a wire with constant power. This limit is determined by the maximum voltage that the wire can handle without overheating or causing damage. If the voltage is increased beyond this limit, the wire may melt or malfunction, leading to a decrease in power and potentially causing a safety hazard.

## 4. Can the power in a wire with constant power and increasing voltage ever decrease?

No, the power in a wire with constant power and increasing voltage cannot decrease. This is because in order for the power to decrease, either the voltage or current must decrease. However, in a wire with constant power, both voltage and current must increase proportionally to maintain the same power. Therefore, the power cannot decrease in this scenario.

## 5. How does the length of the wire affect the power and voltage in this scenario?

The length of the wire does not directly affect the power and voltage in this scenario. However, a longer wire may have a higher resistance, which can cause a decrease in voltage as the current increases. This can impact the overall power in the wire, but it is not a direct effect of the length of the wire. Other factors such as the material and thickness of the wire also play a role in determining the resistance and ultimately, the power and voltage in the wire.

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