A piece of Nichrome wire has a radius of 8.0 10-4 m. It is used in a laboratory to make a heater that dissipates 2.00 102 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

Can you look up the resisitivity of nichrome?

Resistance= resitivity*deltaLength/area

The resistance should be determined by the power and voltage....R=V^2 /power

Please tell me where I went wrong.

R= V^2/power
R= 120V^2/2.00x10^2
R= 72

Resistance = restivity x delta Length/ area

72 = (100x10^-8)(delta length/ pi r^2)

72 = 9100x10^-8) (delta length/ 0.000002011)

72 - (100x10^-8)*(0.000002011) = deltaL

0.000144792 = delta Length

72 * PI * (8E-4^2) * (1 / 9 100E-8) = 1.59 metes

To estimate the necessary length of wire, we need to use the formula for power dissipation in a wire, which is given as:

P = (I^2) * R

Where P is the power dissipated, I is the current flowing through the wire, and R is the resistance of the wire.

To find the necessary length of wire, we first need to calculate the resistance of the wire using the given information. The resistance of a wire can be calculated using the formula:

R = (ρ * (L/A))

Where R is the resistance, ρ is the resistivity of the material (Nichrome wire in this case), L is the length of the wire, and A is the cross-sectional area of the wire.

The resistivity of Nichrome wire is typically given as 1.10 x 10^-6 Ω/m.

The cross-sectional area of the wire (A) can be calculated using the formula:

A = π * r^2

Where A is the cross-sectional area, π is pi (approximately 3.14159), and r is the radius of the wire.

Let's plug in the values into the formulas to find the necessary length of wire:

First, calculate the cross-sectional area of the wire:

A = π * (8.0x10^-4)^2 = 6.35 x 10^-7 m^2

Now, calculate the resistance of the wire:

R = (1.10x10^-6) * (L / 6.35x10^-7)

The power dissipation is given as 2.00x10^2 W.

P = (I^2) * R

We can rearrange this equation to solve for current (I):

I = sqrt(P/R)

Substituting the given values:

I = sqrt(2.00x10^2 / (1.10x10^-6 * (L / 6.35x10^-7)))

Now we can solve for current (I). Since we have the voltage (120 V) and can use Ohm's law (V = I * R), we can solve for current:

120 = I * R

I = 120 / R

Substituting I = 120 / R into the previous equation:

sqrt(2.00x10^2) / sqrt((1.10x10^-6) * (L / 6.35x10^-7)) = 120 / R

Now, we can simplify the equation:

sqrt(200) / sqrt((1.10x10^-6) * (L / 6.35x10^-7)) = 120 / R

Canceling out the square root:

sqrt(200) * sqrt((1.10x10^-6) * (6.35x10^-7)) = 120 / R

Simplifying further:

sqrt(200 * 1.10x10^-6 * 6.35x10^-7) = 120 / R

Now, we can solve for R:

120 / sqrt(200 * 1.10x10^-6 * 6.35x10^-7) = R

Once we have the value for R, we can substitute it into the initial equation for resistance (R = ρ * (L / A)) to solve for the length of the wire (L).