Question

A carbon filament has resistance of 120$\Omega$ at $0^{0}C$. The resistance of a copper filament connected in series with carbon so that the combination has same resistance at all temperatures must be
$\alpha$ of carbon $=-7\times {10}^{-4}{/}^{0}C$; $\alpha$ of copper $=4\times {10}^{-3}{/}^{0}C$

• A. 120$\Omega$
• B. 21$\Omega$
• C. 60$\Omega$
• D. 210$\Omega$

Answer 1

The correct option is B 21$\Omega$

$R_{ca}=R_{ca}^0(1+{\alpha }_{ca}\Delta T)$

$R_{cu}=R_{cu}^0(1+{\alpha }_{cu}\Delta T)$
$R_{ca}+R_{cu}=R_{ca}^0+R_{cu}^0+\Delta T(R_{ca}^0{\alpha }_{ca}+R_{cu}^0{\alpha }_{cu})$

$\Rightarrow R_{ca}+R_{cu}$ is independent of temperature

$\Rightarrow R_{ca}^0{\alpha }_{ca}+R_{cu}^0{\alpha }_{cu}=0$
$120\times 7\times {10}^{-4}=R_{cu}^0\times 4\times {10}^{-3}$

$R_{cu}^0=21\Omega$