Question

If a copper wire has a resistance of 23.7 Ω at a temperature of 20.3 oC, what resistance does it have at 79.0 oC? (Neglect any change in length or cross-sectional area resulting from the change in temperature.)

Answer 1

`R_(79) = 28.91 OHM`

Step-by-step explanation:

Resistance ca be determine by using following formula

`R = R_(ref)\left [ 1+ \alpha (T - T_(ref)) \right ]`

where

R = Conductor resistance = 23.7Ω

Rref = conductor reistance at reference temperature,

α = temperature coefficient of resistance for material, for copper 40.41*10^{-4}

T = Conductor temperature in Celcius = 20.3°C

Tref = reference temperature at which α is specified.

`23.7 = R_(ref)\left [ 1+ 40.41*10^(-4) (20.3) \right ]`
`R_(ref) =21.92 OHM`

now for 79 degree celcius

`R_(79) = R_(ref)\left [ 1+ \alpha (T - T_(ref)) \right ]`

`R_(79) =21.92\left [ 1+ 40.41*10^(-4) (79) \right ]`

`R_(79) = 28.91 OHM`