The resistance of a wire is 5 ohm at `50^@C` and 6 ohm at `100^@C`. The resistance of the wire at `0^@C` will be

Options

A. 1 ohm
B. 5 ohm
C. 3 ohm
D. 2 ohm

Answer

B

Explanation

Temperature dependence of resistance can be written as `R_(t) = R_(0) (1 + alpha t)` We can rearrange the above expression as follows:
`alpha = (R_(t) - R_(0))/(R_(0)t)`
We can equate the value of temperature coefficient of resistance from two sets of values given to us.
`alpha (R_(100) - R_(0))/(R_(0)(100)) = (R_(50) - R_(0))/(R_(0)(50))`
`rArr (6-R_(0))/(2)`
`= (5-R_(0))/(1)`
`rArr 6-R_(0) = 10 - 2R_(0)`
`rArr R_(0) = 4 Omega`
Hence option (b) is the correct option