Question

The resistance of a wire is 5 ohm at ${50}^{\circ }$C and 6 ohm at ${100}^{\circ }$C. The resistance of the wire at $0^{\circ }$C will be:

• A. 2 ohm
• B. 1 ohm
• C. 4 ohm
• D. 3 ohm

Answer 1

Answer: (C)

$R=R_0(1+\alpha \Delta T)$

$R$ at ${100}^{0}C=6\Omega$

$R$ at ${50}^{0}c=5\Omega$

$\Rightarrow \frac{5}{(1+\alpha (50\left)\right)}=\frac{6}{(1+\alpha (100\left)\right)}$

$\Rightarrow 6(1+\alpha (50\left)\right)=5(1+\alpha (100\left)\right)$

$\Rightarrow \alpha =\frac{1}{200}$

$R=R_0(1+\alpha \Delta T)$

$R$ at ${50}^{0}C=5\Omega$

$R_0$ at $0^{0}C=R_0$

$\Rightarrow R=R_0(1+\frac{1}{200}\times 50)$

$\Rightarrow 5=R_0(1+\frac{1}{200}\times 50)$

$\Rightarrow R_0=4\Omega$