Question

The resistance of a wire is $5Î\copyright$ at $50{}^{∘}C$ and $6Î\copyright$ at $100{}^{∘}C$. The resistance of the wire at $0{}^{∘}C$ will be

• A. $3Î\copyright$
• B. $2Î\copyright$
• C. $1Î\copyright$
• D. $4Î\copyright$

Answer 1

Answer: (D)

$R_t=R_0(1+Î\pm t)$
Where $R_t=$ resistance of a wire at $t{}^{∘}C,R_0=$ resistance of a wire at $0{}^{∘}C$, $Î\pm =$ temperature coefficient of resistance.
$∴R_{50}=R_0[1+Î\pm 50]$
and $R_{100}=R_0[1+Î\pm 100]$
or $R_{50}−R_0=R_0Î\pm (50)$
$R_{100}−R_0=R_0Î\pm (100)$
Dividing (i) by (ii), we get
$\frac{5−R_0}{6−R_0}=\frac{1}{2}$
or $10−2R_0=6−R_0$
or $R_0=4Î\copyright$