Question

The resistance of carbon filament at $0^{\circ }$C is $104\Omega$. It is connected in series to an iron wire. The temperature coefficient of resistance of carbon and iron are $-0.0003/{}^{\circ }$C and $+0.0052/{}^{\circ }$C respectively. What must be the resistance of iron wire so that the combined resistance does not change with temperature?

• A. $15\Omega$
• B. $6\Omega$
• C. $15\Omega$
• D. $156/104\Omega$

Answer 1

The correct option is B $6\Omega$

Decrease in resistance of carbon=increase in resistance of iron
$-R_1{\alpha }_{1}t=R_2{\alpha }_{2}t$
$-R_1{\alpha }_1=R_2{\alpha }_2$
$-104\times -0.0003=R_2\times 0.0052$
$R_2=6\Omega$