The resistance of a given electric device is 46 ohms at
0
25 C
. If the
temperature coefficient of resistance of the material is 0.004545 at
0
20 C.
Solve for the temperature of the device when its resistance is 92 ohms?�
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To solve for the temperature of the device when its resistance is 92 ohms, we can use the formula for calculating the change in resistance with temperature:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 is the final resistance (92 ohms)
R1 is the initial resistance (46 ohms)
α is the temperature coefficient of resistance (0.004545)
T2 is the final temperature (unknown)
T1 is the initial temperature (25 C)
Let's substitute the known values into the formula:
92 = 46 * (1 + 0.004545 * (T2 - 25))
Now we can solve for T2:
1 + 0.004545 * (T2 - 25) = 92 / 46
1 + 0.004545 * (T2 - 25) = 2
Simplifying the equation:
0.004545 * (T2 - 25) = 2 - 1
0.004545 * (T2 - 25) = 1
Dividing both sides of the equation by 0.004545:
T2 - 25 = 1 / 0.004545
T2 - 25 = 219.77
Adding 25 to both sides of the equation:
T2 = 219.77 + 25
T2 = 244.77
Therefore, the temperature of the device when its resistance is 92 ohms is approximately 244.77 degrees Celsius.
To solve for the temperature of the device when its resistance is 92 ohms, we can use the equation for the temperature coefficient of resistance:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R1 is the initial resistance (46 ohms)
R2 is the final resistance (92 ohms)
α is the temperature coefficient of resistance (0.004545)
T1 is the initial temperature (25°C)
T2 is the final temperature (unknown, to be solved)
Rearranging the equation to solve for T2, we have:
T2 = (R2/R1 - 1) / α + T1
Plugging in the values, we get:
T2 = (92/46 - 1) / 0.004545 + 25
T2 = (2 - 1) / 0.004545 + 25
T2 = 0.9955 / 0.004545 + 25
T2 = 219.24 + 25
T2 = 244.24°C
Therefore, the temperature of the device when its resistance is 92 ohms is approximately 244.24°C.