Question

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

• A. 15
• B. 6
• C. 1.5
• D. 156

Answer 1

The correct option is B 6

Given: The resistance of carbon filament at $0^{\circ }$ is $104\Omega$ . It is connected in series to an iron wire. The temperature coefficient of resistivity of carbon and iron are $-0.0003$ and $+0.0052$ per degree Celsius respectively.

To find the resistance of iron wire so that the combined resistance does not change with temperature

Solution: Combined resistance will not change if the total resistance of the two rods are in series with change in temperature is zero.

Resistance of the iron at zero temperature $\times$ temperature coefficient $+$ resistance of the carbon at zero temperature \times temperature coefficient $=0$

$⟹R_I{\alpha }_I+R_C\times {\alpha }_C=0⟹R_I\times \left(0.0052\right)+104\times (-0.0003)=0⟹R_I=\frac{0.0312}{0.0052}⟹R_I=6\Omega$

is the resistance of iron wire so that the combined resistance does not change with temperature