At room temperature `(27.0^@C)` the resistance of a heating element is `100 Omega`. What is the temperature of the element if the resistane is found to be `117 Omega`, given that the temperature co-efficicent of the material of the resistor is `1.70 xx 10^(-4) .^@C^(-1)`.
Text Solution
AI Generated Solution
To solve the problem, we will use the formula for the resistance of a conductor as a function of temperature:
\[ R_t' = R_t \times (1 + \alpha \Delta T) \]
Where:
- \( R_t' \) is the resistance at the new temperature (117 Ω)
- \( R_t \) is the resistance at the reference temperature (100 Ω)
- \( \alpha \) is the temperature coefficient of resistance (1.70 × 10^(-4) °C^(-1))
...
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