# What is the Optimal Diameter for a 12.0 Ω Nichrome Wire at 20°C?

• phy112
In summary, to determine the diameter of nichrome wire with a resistance of 12.0 Ω at 20°C, use the equation R=\rho(L/A) and solve for A. Then, use A=1/4pi(dsquared) to find the diameter of the wire. Don't forget to include units in your calculations.
phy112

## Homework Statement

If 46 m of nichrome wire is to have a resistance of 12.0 Ω at 20°C, what diameter wire should be used?

## Homework Equations

R=$$\rho$$(L/A)

## The Attempt at a Solution

I tried and I got 2.1. The $$\rho$$ of nichrome is 108e-8

First solve for the variable you are looking for and put it on one side. Keep your knowns on the other side. Remember that A stands for area, and area is related to wire diameter.

I am online for a bit, so give it a go. DON'T FORGET YOU UNITS!

ok yeah i got 2.3 mm. after i figured out A. I figured out diameter doing A=1/4pi(dsquared)

ok i got it right. thanks!

Good for you!

## 1. What is the relationship between diameter and resistance?

The relationship between diameter and resistance is inverse, meaning that as the diameter of a material increases, the resistance decreases. This is because a larger diameter allows for more space for electrons to flow, resulting in less resistance to the flow of electricity.

## 2. How does the length of a material affect its resistance?

The longer a material is, the higher its resistance will be. This is because a longer material has more atoms, which creates more obstacles for electrons to pass through, resulting in higher resistance.

## 3. What unit is used to measure resistance?

Resistance is measured in ohms (Ω). This unit is named after the German physicist Georg Ohm, who discovered the relationship between voltage, current, and resistance.

## 4. How does temperature affect resistance?

As temperature increases, so does the resistance of a material. This is because as temperature rises, the atoms in the material vibrate more, creating more obstacles for electrons to flow through, resulting in higher resistance.

## 5. What is the formula for calculating resistance?

The formula for calculating resistance is R = V/I, where R is resistance in ohms, V is voltage in volts, and I is current in amperes. This formula is known as Ohm's law and is used to determine the resistance of a material based on its voltage and current.

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