Question

If resistance of wire at $ 50{}^\circ C $ is $ 5R\,\Omega $ and at $ 100{}^\circ C $ is $ 6R\,\Omega . $ find resistance of $ 0{}^\circ C $ :

• A. $ 0R\,\,\Omega $
• B. $ 2R\,\,\Omega $
• C. $ 3R\,\,\Omega $
• D. $ 4R\,\,\Omega $

Answer 1

Answer: (D)

$R_{t} =R_{0}(1+\alpha \Delta t)$
$\therefore 5 R =R_{0}(1+\alpha \times 50)\ldots$(i)
and $ 6 R =R_{0}(1+\alpha \times 100) \ldots$(ii)
On dividing Eq. (i) by (ii) and solving it, we get
$\alpha=\frac{1}{200} \Omega / 0^{\circ} C$
On putting in Eq. (i), we get
$ 5 R =R_{0}\left(1+\frac{1}{4}\right) $
$ \Rightarrow 5 R =\frac{5}{4} R_{0} $
$ \Rightarrow R_{0}=4 R\, \Omega$