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

Answer:

$R_{79} = 28.91 OHM$

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

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

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

$R_{79} = 28.91 OHM$