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Home / Doubts and Solutions/JEE/Physics

A carbon and an aluminium wire are connected in series. If the combination has resistance of 30 ohm at 0degree Celsius. what is the resistance of carbon and aluminium wire at 0 degree Celsius so that the resistance of the combination does not change with temperature

Asked by khedejalaj7 24th September 2018, 10:47 AM
Answered by Expert
Answer:
Variation of resistance R with temperature is given by,  R = R0(1+α×T).................(1)
 
where R0 is the resistance at 0°C , α is the temperature coefficient of resistivity and T is temperature.
 
Let RC and RAl are resistance of Carbon wire and Aluminium wire respectively at Temperature T.
Let RC0 and RAl0 are resistance of Carbon wire and Aluminium wire respectively at 0ºC .
 
then RC + RAl = RC0(1+αC×T) + RAl0(1+αAl×T)  ...................(2)
 
if we consider that combined resistance will not change with temperature, then we can simplify eqn.(2) as,   RAl0 × αAl = - RC0 × αC
 
RAl0 /RC0    =  - αC / αAl = 4.8×10-4 / 4.29 ×10-3  = 0.112  or RAl0  = 0.112×RC0 .................(3)
 
we have  RAl0   +  RC0 = 30Ω .......................(4)
 
from eqn.(3) and (4) we get RC0 = 27Ω and RAl0 = 3Ω
Answered by Expert 24th September 2018, 1:08 PM
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