Question

The resistance of a wire at 20⁰C is 20 Ω and at 500⁰Cis 60Ω. At which temperature resistance will be 25Ω

• A. 50⁰C
• B. 60⁰C
• C. 70⁰C
• D. 80⁰C

Answer 1

Answer: (D)

80⁰C

Answer 2

By using $\frac { R _ { 1 } } { R _ { 2 } } = \frac { \left( 1 + \alpha t _ { 1 } \right) } { \left( 1 + \alpha t _ { 2 } \right) } \Rightarrow$

$\frac{20}{60} = \frac{1 + 20\alpha}{1 + 500\alpha} \Rightarrow \alpha = \frac{1}{220}$

Again by using the same formula for 20Ω and 25Ω ⇒ $\frac{20}{25} = \frac{\left( 1 + \frac{1}{220} \times 20 \right)}{\left( 1 + \frac{1}{220} \times t \right)}$ ⇒ t = 80⁰C