Name: Resistance of a Conductor
Uploaded: 2019-07-19
Duration: 4 min 54 s
Description: Ever wondered why conductors give out heat when current passes through them? This is due to hindrance to the flow of electric charge. Let’s find out more in...

Question

The resistance of a carbon filament at

0 ° C

is

104 Ω

. What should be the resistance of an iron filament which should be connected in series with the carbon filament so that the resistance of the combined filament does not change with temperature? The temperature coefficient of resistance of iron is

α = + 0.0052 ° C^{- 1}

and of carbon is

- 0.0003 ° C^{- 1}

.

Accepted Answer

Here the expression of resistance at any temperature is expressed as $R_{T} = R_{0} + R_{0} αΔT$

For carbon, $R_{TC} = R_{oc} + R_{oc} α_{c} {ΔT}_{c}$

For Iron, $R_{Tfe} {= R}_{o, F e} {+ R}_{oFe} α_{fe} {ΔT}_{f e}$

Here the carbon & Iron resistance are connected in series and the equivalent resistance is deserved to be temperature independent .

So, the temp dependent terms of both resistors must cancel out each other.

i.e. $R_{oC} α_{c} {ΔT}_{c} = R_{oFe} α_{fe} {ΔT}_{f e}$

$R_{0 (Fe)} = \frac{R_{0 C} α_{c}}{α_{Fe}}$ $= \frac{104 \times 3 \times 10^{- 4}}{52 \times 10^{- 4}} = 6 Ω$

So, Resistance of iron at $0^{o} C$ Should be $6 Ω$ .

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