A carbon and an aluminium wire are connected in series. If the combination has resistance of 30 ohms at 0°c what is the resistance of carbon and aluminium wire at 0°c so that the resistance of the combination does not change with temperature ( alpha for carbon = -0.5×10^-3℃^-1 and alpha for aluminium = 4+×10^-3℃^-1
Asked by Jalajkhede11
24th July 2018,
10:04 AM
Answered by Expert
Answer:
Let RC and RAl be resistances made of carbon and Aluminium respectively at 0ºC.
We are given that, RC + RAl = 30 Ω .................(1)
Series combination of these rseistances at a raised temperature ΔT = RC(1+αC×ΔT) + RAl(1+αAl×ΔT).............(2)
Since the resistance of combination does not chnage with increase of temperature, from eqn.(1) and (2), we have
RC + RAl = RC(1+αC×ΔT) + RAl(1+αAl×ΔT)
RC(αC×ΔT) + RAl(αAl×ΔT) = 0
from eqn.(1) and (3), we get RAl = (10/3) Ω and RC = (80/3) Ω
Answered by Expert
25th July 2018,
11:59 PM
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