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Displacement Current

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Question

The resistance of a carbon filament at 0ºC is 104 ohm. It is connected in series to an iron wire. The temperature coefficient of resistivity of carbon and iron are —0.0003 and +0.00052 per ºC respectively. What must be the resistance of the iron wire so that the combined resistance does not change with temperature?

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Solution

Combined resistance will not change if the total resistance of two rods in series with change in temperature is zero.
$R e s i s \tan c e o f t h e i r o n a t z e r o t e m p \times t e m p . c o e f f i c i e n t + R e s i s \tan c e o f t h e c a r b o n a t z e r o t e m p \times t e m p . = 0 R_{I} α_{I} + R_{C} α_{C} = 0 R_{i} = \frac{- 104 \times 0.0003}{0.00052} = 60 o h m$

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