A 1.50 m cylindrical rod of diameter 0.550 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0 C) the ammeter reads 18.8 A, while at 92.0 C it reads 17.4 A. You can ignore any thermal expansion of the rod.
1.Find the resistivity and for the material of the rod at 20 C. (rho= ? Ω*m)2.Find the temperature coefficient of resistivity at 20 C for the material of the rod.α= ? (C)^-1)

The answer to the questions are:

1. The resistivity for the material of the rod at 20 °C (ρ) is                                                

     .

2. The temperature coefficient of resistivity at 20 °C for the material of the              

    rod(α) is .

Given to us:

Voltage across the rod, V = 15.0 V

Length of rod, L = 1.5 m = 150 cm,

Diameter, d = 0.55 cm,

Initial temperature,  

current at ,  

Final temperature,  

current at ,  

1.) To find out the resistivity of the rod(ρ),

Resistant of the rod(R),

Resistivity of the rod at (ρ),

Hence, the resistivity for the material of the rod at 20 °C (ρ) is  .

2.) To find out the temperature coefficient of resistivity at 20°C for the material of the rod (α) can be gotten from the equation,

we need resistant of the rod(),

Now, solving to get the value of α

Hence, the temperature coefficient of resistivity at 20 °C for the material of the rod(α) is .

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α = 1.114 × 10⁻³ (°C)⁻¹

Explanation:

Given that:

Length of rod (L) = 1.5 m,

Diameter (d) = 0.55 cm,

Area (A) =

Radius (r) = d / 2 = 0.275 cm,

Voltage across the rod (V) = 15.0 V.

At initial temperature (T₀) = 20°C, the current (I₀) = 18.8 A while at a temperature (T) = 92⁰C, the current (I) = 17.4 A

a) The resistance of the rod (R) is given as:

Therefore the resistivity and for the material of the rod at 20 °C (ρ) is:

b) The temperature coefficient of resistivity at 20°C for the material of the rod (α) can be gotten from the equation:

Rearranging to make α the subject of formula:

it is a negative acceleration