At what temperature will the resistance of a copper wire become three times its value at 0° C ? (temperature coefficient of resistance for copper .=4 × 10-3 / ° C )

Question

At what temperature will the resistance of a copper wire become three times its value at 0° C ? (temperature coefficient of resistance for copper .=4 × 10-3 / ° C ) (A) 400° C (B) 450° C (C) 500° C (D) 550° C

Tardigrade Admin · Accepted Answer

From definition of temperature resistance coefficient Rt =R0(1+α t) 3 R0 =R0(1+4 × 10-3 t) 3=1+4 × 10-3 t 4 × 10-3 t=2 t= (2/4 × 10-3) =500° C

Q. At what temperature will the resistance of a copper wire become three times its value at $0^{\circ} C$ ? (temperature coefficient of resistance for copper $= 4 \times 1 0^{- 3} /^{\circ} C)$

$40 0^{\circ} C$

$45 0^{\circ} C$

$50 0^{\circ} C$

$55 0^{\circ} C$

From definition of temperature resistance coefficient
$R_{t} = R_{0} (1 + α t)$
$3 R_{0} = R_{0} (1 + 4 \times 1 0^{- 3} t)$
$3 = 1 + 4 \times 1 0^{- 3} t$
$4 \times 1 0^{- 3} t = 2$
$t = \frac{2}{4 \times 1 0 ^{- 3}}$
$= 50 0^{\circ} C$

Q. At what temperature will the resistance of a copper wire become three times its value at 0∘C ? (temperature coefficient of resistance for copper =4×10−3/∘C)

400∘C

450∘C

500∘C

550∘C