00:01
We know that resistance r is related with change in temperature by the formula r0 into 1 plus alpha delta t, where alpha is the coefficient of temperature and delta t is the change in temperature.
00:26
Now, we know that at 20 degrees celsius resistivity of the wire, let's say r or r, r, r0, is given as 1 .59 into 10 to the power minus 8 meter.
00:48
O.
00:51
So, we know that resistance, the formula for the cylindrical resistance wire is given as resistance r equals to row not into length divided by area where area this area is the area of cross -section of the wire.
01:11
Our resistance at 20 degrees celsius is given as 30 -oom.
01:18
Ro -not that is the resistivity of the wire is 1 .59 into 10 to the power minus 8.
01:25
Length of the wire is given 1 .2 meter.
01:28
So area of cross -section can be written.
01:30
As pi r square so solving for r we will get the radius of the wire equals to solving this we will get 014 m m so this will be the radius of the wire for the given data now in the second part that is part b it has been asked that what will be the assistance of the same wire at 10 degrees celsius.
02:08
Now using the equation this r equals to r0 into 1 plus alpha t, alpha delta t.
02:16
Now here delta t equals to t2 minus t1.
02:24
Now it has been given that final temperature t2 is 10 degrees celsius so we can write 10 degrees celsius minus 20 degrees celsius which is the reference temperature.
02:39
So, solid.
02:40
Solving this will get delta t equals to minus 10 degrees celsius.
02:45
Now putting these values will get r equals to r0 where r0 is 30 om, 1 plus alpha that is equals to .0038 into minus 10 which we calculated this time soon.
03:03
So solving for this we will get r equals to 28 .86 oom.
03:10
So, resistance of the wire will be at 10 degrees celsius will be 28 .86.
03:21
Now we can also write r equals to r0 into 1 plus alpha delta t.
03:28
Now replacing r equals to row into l by a, we can write row into l by a equals to row not into l by a into 1 plus alpha delta t.
03:43
Now this will cancel out so it will become resistivity equals to resistivity not or r0 into 1 plus alpha delta t.
03:53
Now putting the values here we'll get now r0 is the 1 .59 into 10 to the power minus 8 oom meter into 1 plus now for 25 degrees celsius delta t will be equals to 5 so it will be 0 .038 5...