Problem 18.79 A fish-tank heater is rated at 85 W when connected to 120 V. The h

Question

Problem 18.79

A fish-tank heater is rated at 85 W when connected to 120 V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 4.0 m .

Part A

What is the diameter of the wire?

Express your answer to two significant figures and include the appropriate units.

Problem 18.79

A fish-tank heater is rated at 85 W when connected to 120 V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 4.0 m .

Part A

What is the diameter of the wire?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

here by using the formula

R = rho * L / A

the resistivity of nichrome wire is rho = 1.1 * 10^-6 ohm m

P = V * I

R = V / I

R = V^2 / P

R = 120^2 / 85

R = 169.4 ohm

then put the values in the formula

169.4 = 1.1 * 10^-6 * 4 / (pie * r^2)

r = sqrt( 1.1 * 10^-6 * 4 / ( pie * 169.4))

r = 9.092 * 10^-5 m

so the diameter of the wire is

d = 2 * 9.092 * 10^-5 = 1.8 * 10^-4 m

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