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
$R_{150}=133\Omega$
$\Rightarrow R_0(1+\alpha t)=133\left[\because R_t=R_0(1+\alpha t)\right]$
$\Rightarrow R_0(1+150\alpha )=\mathrm{133...}(i)$
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, $\alpha =0.0045^{\circ }{C}^{-1}$]
$=\frac{43225}{1.675}=258.06\Omega =258\Omega$