A silver wire 2m long is to have a resistance of 0.5Ω.what should its diameter be ? Given (ρ=1.52×10^-8Ωm) Physics class 12th problem solution Inter class physics problem solution Electrodynamics Problem Solution Current electricity problems solution
00:00Question is a silver wire 2 meter long is to have a resistance of 0.5 ohm. What should
00:16its diameter be? Is resistivity of wire is given which is 1.52 into 10 raised power minus
00:248 ohm into meter. So first of all we will make a data is the length of wires is obtained
00:43as 2 meter and resistance is obtained as 0.5 ohm. We have to find the diameter of wire
01:03means d and resistivity rho is obtained as 1.52 into 10 raised power minus 8 ohm into meter.
01:22So for solution is r is equal to rho into L upon area. So when we will take area on the
01:50other side of equal then it will multiply. So it will be area into resistance will be
01:58equal to rho into L. So area will be equal to rho into L upon when we will take R on the
02:11other side of equal then it will divide. As the shape of wire is circular. So the area of
02:26wires is calculated is calculated by using formula pi R square. So pi R square will be equal
02:36to rho into L upon R is R square will be equal to rho into L upon pi into R. Because when we
02:56will take pi we will take pi on the other side of pi on the other side of equal then it will divide.
03:01Then it will divide. Because here it is multiplying with R square. So we have to find R means radius.
03:08So R will be equal to under root rho into L upon pi into R. Because when we will remove the square then it will be
03:24square root on the other side of equal. First of all we will find radius because diameter is equal to 2R. So radius will be equal to by putting the given values
03:49is resistivity is 1.52 into 10 raised power minus 8 multiplied with length which is 2 meter divided by pi. The value of pi is 3.14 into
04:130.5 into resistance which is 0.5 ohm. So radius will be obtained as 1.52 into 2. It will be 3.04 into 10 raised power minus 8 divided by 3.14 into 0.5 it will be 1.57.
04:42So after simplification we will get the radius is 1.93 into 10 raised power minus 8. So after getting the square root of 1.93 we will get 1.39
05:111 into 10 raised power minus 8 is 10 raised power minus 4. So meter is we have obtained the value of radius. So now diameter is diameter is equal to 2R.
05:371.94 into 10 raised power minus 4. So diameter will be obtained as 2.783 into 10 raised power minus 4 meter. So this is our required answer.
