A wire has resistance of 3.1 `Omega ` at `30 ^@` C and `4.5 Omega` at `100 ^@ C` . The temperature coefficient of resistance of the wire is

Options

A. `0.0012^@c^-1`
B. `0.0024^@C^-1`
C. `0.0032^@C^-1`
D. `0.0064^@C^-1`

Answer

D

Explanation

Answer (4) `R_1 = 3.1 Omega, t_1 = 30^@C`
`R_2 = 4.5Omega, t_2 = 100^@C` .
Temperature coefficient of resistance of wire, `alpha = (R_2 - R_1)/ (R_1[t_2 - t_1]) = (4.5 - 3.1)/ ((3.1) [(100) - (30)])` .
`Rightarrow alpha = 6.45 xx 10^(-3@) C^-1`.
`alpha = 0.0064 C^-1`