Question

A resistance thermometer has resistance \(95\ \Omega\) at the ice point and \(140\ \Omega\) at the steam point. The resistance obtained if the actual temperature is \(30^{\circ }\text{C}\) is

• A. \(117.5\ \Omega\)
• B. \(108.5\ \Omega\)
• C. \(113.5\ \Omega\)
• D. \(13.5\ \Omega\)

Hint:

Resistance varies linearly with temperature between the ice point and the steam point.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A resistance thermometer is linear between the fixed points: \(\dfrac{R_t-R_0}{R_{100}-R_0}=\dfrac{t}{100}\).

Step 2: Substitute the data
\(R_0=95\ \Omega\), \(R_{100}=140\ \Omega\) and \(t=30^{\circ}\text{C}\).
\(\dfrac{R_t-95}{45}=\dfrac{30}{100}\).

Step 3: Calculation
\(R_t=95+0.3\times 45=95+13.5=108.5\ \Omega\).
The value \(13.5\ \Omega\) is only the increase, not the resistance.

Final Answer:
The resistance at \(30^{\circ}\text{C}\) is \(108.5\ \Omega\). \[ \boxed{\text{(B) }108.5\ \Omega} \]