Question

The resistance of a wire at ${20}^{\circ }C$ is $20\Omega$ and at ${500}^{\circ }C$ is $60\Omega$. At which temperature resistance will be $25\Omega$?

• A. ${50}^{\circ }C$
• B. ${60}^{\circ }C$
• C. ${70}^{\circ }C$
• D. ${80}^{\circ }C$

Answer 1

Answer: (D)

${80}^{\circ }C$.

Step 1: Given

Resistance of wire at ${20}^{\circ }C$ = $20\Omega$

Resistance of wire at ${500}^{\circ }C$ = $60\Omega$

Step 2: Formula used and calculation of temperature

The value of resistance at any temperature $T$ is given by,

RT=R0(1+αT)R_T=R_0(1+\alpha T)$R_T=R_o(1+\alpha T)$

where $\alpha$ = Temperature coefficient of resistance.

$\Rightarrow \frac{R_1}{R_2}=\frac{(1+\alpha t_1)}{(1+\alpha t_2)}$

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

$\Rightarrow \alpha =\frac{1}{220}$
Again by using the same formula for $20\Omega$ and $25\Omega$

⇒2025=(1+1220×20)(1+1220×t)\Rightarrow \frac{20}{25} = \frac{( 1+\frac{1}{220} \times 20)}{(1+\frac{1}{220} \times t)}$\Rightarrow \frac{20}{25}=\frac{1+\frac{1}{220}\times 20}{1+\frac{1}{220}T}$

$\Rightarrow T={80}^{\circ }C$.

Hence the temperature is ${80}^{\circ }C$.

Hence, option C is correct.