Question:
In resistance thermometer, the resistance at \(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) are \(6.74 \Omega\) and \(7.74 \Omega\) respectively. The temperature corresponding to \(6.53 \Omega\) resistance is
In resistance thermometer, the resistance at \(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) are \(6.74 \Omega\) and \(7.74 \Omega\) respectively. The temperature corresponding to \(6.53 \Omega\) resistance is
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Resistance varies linearly with temperature, so use the change per degree between 0 and 100 degrees Celsius.
Updated On: Nov 13, 2026
\(+53^{\circ}\mathrm{C}\)
\(+21^{\circ}\mathrm{C}\)
\(-53^{\circ}\mathrm{C}\)
\(-21^{\circ}\mathrm{C}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Resistance varies linearly with temperature: \(\dfrac{R_t - R_0}{R_{100} - R_0} = \dfrac{t}{100}\).
Step 2: Substitute
\(R_0 = 6.74\ \Omega\), \(R_{100} = 7.74\ \Omega\), \(R_t = 6.53\ \Omega\)
Step 3: Calculation
\(\dfrac{6.53 - 6.74}{7.74 - 6.74} = \dfrac{-0.21}{1.00}\), so \(t = -21^{\circ}\text{C}\).
Step 4: Result
Option D.
Final Answer:
The temperature is minus 21 degrees Celsius. \[ \boxed{\text{(D) }-21^{\circ}\text{C}} \]
Resistance varies linearly with temperature: \(\dfrac{R_t - R_0}{R_{100} - R_0} = \dfrac{t}{100}\).
Step 2: Substitute
\(R_0 = 6.74\ \Omega\), \(R_{100} = 7.74\ \Omega\), \(R_t = 6.53\ \Omega\)
Step 3: Calculation
\(\dfrac{6.53 - 6.74}{7.74 - 6.74} = \dfrac{-0.21}{1.00}\), so \(t = -21^{\circ}\text{C}\).
Step 4: Result
Option D.
Final Answer:
The temperature is minus 21 degrees Celsius. \[ \boxed{\text{(D) }-21^{\circ}\text{C}} \]
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