In a single core PVC cable, copper conductor diameter is 0.9 mm, PVC insulation thickness is 0.8 mm. Find out the weight of PVC per KM of cable (density of PVC is 1.5gm/CC)
Answers
Answer:
In cross -section, the cable consists of a central circular conductor surrounded by a circular PVC insulator.
To determine the area of the PVC insulation only we need to subtract the area occupied by the central wire from the overall cable area.
The overall radius of the cable is the radius of the central conductor + the thickness of the PVC insulator
Overall radius of the cable is:- (0.9mm/2 + 0.8mm) = 1.25 mm or 1.25 x 10^-3 m
So, to find the total area occupied by the PVC only we do two subtractions
Cross- sectional area of PVC, Apvc = cross sectional area of cable, Ac minus the cross- sectional area of the wire, Aw.
cross sectional area of cable, Ac = pi x r^2 = pi x (1,25 x 10^-3)^2= 4.909375 x 10^-6 m^2
cross sectional area of inner wire, Aw = pi x (0.45 x 10^-3)^2 =6.36255 x 10^-7 m^2
Therefore, cross sectional area of PVC = Ac-Aw
Apvc =Ac-Aw = 4.909375 x 10^-6 - 6.36255 x 10^-7
Apvc = 4.27312 x 10^-6 m^2
To get the total volume of PVC used over 1km we multiply the area by the length of the cable
Vpvc =4.27312 x 10^-6 x 1000
Vpvc = 4.27312 x 10^-3 m^3
Density = mass/volume
Mass of PVC = density of PVC x Vpvc
Density of PVC = 1.5 gm per cc, Or..
Denity of PVC = 1.5 x 10^6 gm per m^3, Or ..
Density of PVC =1.5 x 10^3 kg/m^3
Total mass of PVC = 1.5 x 10^3 x 4.27312 x 10^-3
Total mass of PVC = 6.40968 kg
Weight of PVC = mass of PVC x 9.81
Weight of PVC = 62.8789
Weight of PVC = 63 N
Explanation: