Question

Of what material is a wire made if it is 25.0 m long with a 0.100 mm diameter and has a resistance of 77.7Ω at 20.0ºC?

a. Copper
b. Aluminum
c. Nichrome
d. Silver

What is the resistance of the wire at 150ºC?
a. 85.4Ω
b. 98.6Ω
c. 102.3Ω
d. 121.5Ω

Answer 1

The wire is made of Copper and its resistance at 150°C is 98.6 ohms.

Step-by-step explanation:

The material of the wire can be determined by analyzing its characteristics such as length, diameter, and resistance. In this case, the wire is 25.0 m long with a diameter of 0.100 mm and a resistance of 77.7 ohms at 20.0°C. By comparing these values with the known properties of different materials, we can conclude that the wire is made of Copper.

To find the resistance of the wire at 150°C, we can use the formula:

R2 = R1 * (1 + α * (T2 - T1))

where R1 and R2 are the resistances at temperatures T1 and T2 respectively, and α is the temperature coefficient of resistance for the material. The temperature coefficient of resistance for Copper is approximately 0.00393 1/°C. Plugging in the values, we get:

R2 = 77.7 * (1 + 0.00393 * (150 - 20)) = 98.6 ohms