Question

Resistance of a tungsten wire at $150^{\circ} C$ is $133\, \Omega$, Its temperature coefficient of resistance is $0.0045^{\circ} C ^{-1}$. The resistance of this wire at $500^{\circ} C$ is

• A. $180\, \Omega$
• B. $225\, \Omega$
• C. $258\, \Omega$
• D. $317\, \Omega$

Answer 1

Answer: (C)

Resistance of tungsten wire at $150^{\circ} C$ is given as
$R_{150}=133\, \Omega$
$\Rightarrow R_{0}(1+\alpha t)=133\,\, \left[\because R_{t}=R_{0}(1+\alpha t)\right]$
$\Rightarrow R_{0}(1+150 \alpha)=133 ...(i)$
Similarly, resistance of wire at $500^{\circ} C$ is given as
$R_{500}=R_{0}(1+500 \alpha)$
$R_{0}(1+500 \alpha)=R_{500} ... (ii)$
From Eqs. (i) and (ii), we get
$\frac{R_{0}(1+150 \alpha)}{R_{0}(1+500 \alpha)}=\frac{133}{R_{500}}$
$\Rightarrow R_{500}=\frac{133(1+500 \alpha)}{1+150 \alpha}$
$=\frac{133(1+500 \times 0.0045)}{1+150 \times 0.0045}$
[given, $\alpha=0.0045^{\circ} C ^{-1}$]
$=\frac{43225}{1.675}=258.06\, \Omega=258\, \Omega$