Question

The resistance of a metallic wire at 0°C is 5ohm.
At what temperature its resistance will be 15ohm?
(The temperature coefficient of resistance of the
metal is 5x10-3/°C.)​

Answer 1

Answer:

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Answer 2

Answer:

At 400°C the resistance of the metallic wire will be 15Ω.

Explanation:

The relation between resistance and temperature is given as,

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

Where,

R=resistance at a specific temperature "T₂"

R₀=resistance at the initial temperature

α=temperature coefficient of resistance

ΔT=change in temperature

From the question we have,

R=15Ω

R₀=5Ω

α=5 ×10⁻³/°C

By substituting the values in equation (1) we get;

$15=5(1+5\times 10^-^3\Delta T)$

$3=1+5\times 10^-^3\Delta T$

$3-1=5\times 10^-^3\Delta T$

$\Delta T=\frac{2}{5\times 10^-^3}$

$\Delta T=400\textdegree C$      (2)

Now,

$T_2-T_1=400\textdegree C$

$T_2-0=400\textdegree C$

$T_2=400\textdegree C$

Hence, at 400°C the resistance of the metallic wire will be 15Ω.

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