A 200-V bulb takes a current of 0.2 A. The length of its filament is 22 cm and the specific resistance of the material of the filament is 7 * 10^-5 ohm-cm. Find the radius of the filament. (pi=22/7)
We know
V=IR
V= 220 V
I= 0.2 A
So R = 220/0.2
R= 1100 ohm
Also R= ρL/A
Where
L= Length = 22cm=0.22m
ρ= 7 x 10-5 ohm-m
so A= ρL/R
A= 7x10-5 x 0.22/1100
A= 1.4x10-8 m2
A= πr2 = 1.4x10-8
r2 = 0.14x10-8 /3.14
r2= 0.44 x 10-8
r=0.667 x10-4 m