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A carbon filament has resistance of 120O...

A carbon filament has resistance of `120Omega` at `0^(@)C` what must be te resistance of a copper filament connected in series with resistance and combined resistance remained constant at all temperature
`(alpha_("carbon")=(-5xx10^(-4))/(``^(@)C),alpha_("copper")=(4xx10^(-3))/(``^(C))`

Text Solution

Verified by Experts

If `R_(0), R_(t)` be the resistance of a wire at `0^@C` and `t^@C` then temperature coefficient of resistance is
`alpha = (R_(t) - R_(0))/R_(0)t`
or change in resistance `= R_(t) - R_(0)=R_(0) alpha t`
Let R be the resistance of copper palced in series with carbon at `0^@C`. If the combination has same resistance at all temperature, then at temperature `t^@C`,
increase in resistance of copper = decrease in resistance of carbon
`:. alpha_(Cu) R t = alpha_(c) R_(0) t`
or `0.004 xx R xx t = 0.0007 xx 100 xx t`
or `R = (0.0007 xx 100)/0.004 = 17.5 Omega`
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