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Resistivity

The resistanc...

Question

The resistance of a conductor is $5$ ohm at $50^{\circ}$ and $6$ ohm at $100^{\circ} .$ What is its resistance at $0^{0}$ ?

A

1

ohm

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B

2

ohm

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C

3

ohm

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D

4

ohm

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Solution

The correct option is D $4$ ohm
$\begin{matrix} A c c o r r d i n g t o q u e s t i o n . . . . . . . . . . . . . . . . . . . . . . . D e p e n d e n c e o f t h e r e s i s t a n c e i s g i v e n, R_{t} = R_{0} (1 + a t) ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} w h e r e R_{t} i s t h e r e s i s t a n c e a t t e m p t . R_{0} i s t h e r e s i s t a n c e a t 0^{0} C a n d a i s t h e t e m p r a t u r e c p e f f i c i e n t, \end{matrix} s o t h a t, 5 = R_{0} (1 + 50 a) 6 = R_{0} (1 + 100 a) n o w, d i v i d i n g t h e s e e q u a t i o n, a = \frac{1}{200} / c e l c i o u s ∴ R_{0} = 4 o h m a n d t h e c o r r e c t o p t i o n i s D . \end{matrix}$

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