Resistance of the wire is measured as 2 Ω and 3 Ω at 10° C and 30° C respectively. Temperature co - coefficient of resistance of the material of the wire is :

Question

Resistance of the wire is measured as 2 Ω and 3 Ω at 10° C and 30° C respectively. Temperature co - coefficient of resistance of the material of the wire is : (A) 0.033° C -1 (B) -0.033° C -1 (C) 0.011° C -1 (D) 0.055° C -1

Tardigrade Admin · Accepted Answer

R = R 0(1+α Δ T ) 3= R 0(1+α(30-0)) 2= R 0(1+α(10-0)) (3/2)=(1+30 α/1+10 α) α=(1/30)=0.033

Q. Resistance of the wire is measured as $2 Ω$ and $3 Ω$ at $1 0^{\circ} C$ and $3 0^{\circ} C$ respectively. Temperature $co -$ coefficient of resistance of the material of the wire is :

$0.03 3^{\circ} C^{- 1}$

$- 0.03 3^{\circ} C^{- 1}$

$0.01 1^{\circ} C^{- 1}$

$0.05 5^{\circ} C^{- 1}$

$R = R_{0} (1 + α Δ T)$
$3 = R_{0} (1 + α (30 - 0))$
$2 = R_{0} (1 + α (10 - 0))$
$\frac{3}{2} = \frac{1 + 30 α}{1 + 10 α}$
$α = \frac{1}{30} = 0.033$

Q. Resistance of the wire is measured as 2Ω and 3Ω at 10∘C and 30∘C respectively. Temperature co− coefficient of resistance of the material of the wire is :

0.033∘C−1

−0.033∘C−1

0.011∘C−1

0.055∘C−1