A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4076 A is precisely measured at 30.0∘C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3502 A. The temperature coefficient of resistivity of aluminum is 0.00429. What is the unknown temperature?

The value of temperature in new environment is 68 degree Celsius.

The resistance is defined as ratio of voltage to the current.

     Resistance,

When voltage is 10.00-V power supply, and a current of 0.4076 A .

Resistance,

When voltage is 10.00-V power supply, and a current of 0.3502A

            ohm

Here we use relationship,

                and  

Where is the temperature coefficient of resistivity.

Substituting all values in above equation

Hence, The value of temperature in new environment is 68 degree Celsius.

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Explanation:

The relationship between voltage, resistance and current in a metal wire is given by

where

V is the voltage

R is the resistance

I is the current

Moreover, the resistance of a metal wire as a function of the temperature is:

(1)

where

is the resistance at temperature

is the temperature coefficient

In this problem, at 30.0∘C, we have

V = 10.00 V

I = 0.4076 A

So the resistance at this temperature is

Then, at the unknown temperature T, the current is

I = 0.3502 A

So the resistance is

Substituting and solving for (1), we find the unknown temperature:

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