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)

$R_t=R_0(1+\alpha \Delta t)$
$\therefore 5R=R_0(1+\alpha \times 50)\dots$(i)
and $6R=R_0(1+\alpha \times 100)\dots$(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
$5R=R_0\left(1+\frac{1}{4}\right)$
$\Rightarrow 5R=\frac{5}{4}{R}_0$
$\Rightarrow R_0=4R\Omega$