A silver wire has temperature coefficient of resistivity 4 × 10-3 / ° C and its resistance at 20° C is 10 Ω. Neglecting any change in dimensions due to the change in temperature, its resistance at 40° C is

Question

A silver wire has temperature coefficient of resistivity 4 × 10-3 / ° C and its resistance at 20° C is 10 Ω. Neglecting any change in dimensions due to the change in temperature, its resistance at 40° C is (A) 0.8 Ω (B)  1.8 Ω (C)  9.2 Ω (D)  10.8 Ω

Tardigrade Admin · Accepted Answer

Given, α=4 × 10-3 / ° C T1 =20° C T2 =40° C R t2 =R t1(1+α Δ t) Δ T =40-0=20° C R t1 =10 Ω R4 Ω =10(1+4 × 10-3 × 20] Ω =10[1+80 × 10-3] =10[1.08]=10.8 Ω

Q. A silver wire has temperature coefficient of resistivity $4 \times 1 0^{- 3} /^{\circ} C$ and its resistance at $2 0^{\circ} C$ is $10 Ω$ . Neglecting any change in dimensions due to the change in temperature, its resistance at $4 0^{\circ} C$ is

$0.8 Ω$

$1.8 Ω$

$9.2 Ω$

$10.8 Ω$

$11.6 Ω$

Given, $α = 4 \times 1 0^{- 3} /^{\circ} C$
$T_{1} = 2 0^{\circ} C$
$T_{2} = 4 0^{\circ} C$
$R t_{2} = R t_{1} (1 + α Δ t)$
$Δ T = 40 - 0 = 2 0^{\circ} C$
$R t_{1} = 10 Ω$
$R_{4} Ω = 10 (1 + 4 \times 1 0^{- 3} \times 20] Ω$
$= 10 [1 + 80 \times 1 0^{- 3}]$
$= 10 [1.08] = 10.8 Ω$

Q. A silver wire has temperature coefficient of resistivity 4×10−3/∘C and its resistance at 20∘C is 10Ω. Neglecting any change in dimensions due to the change in temperature, its resistance at 40∘C is

0.8Ω

1.8Ω

9.2Ω

10.8Ω

11.6Ω

Given, α=4×10−3/∘C T1​=20∘C T2​=40∘C Rt2​=Rt1​(1+αΔt) ΔT=40−0=20∘C Rt1​=10Ω R4​Ω=10(1+4×10−3×20]Ω =10[1+80×10−3] =10[1.08]=10.8Ω