Answer:
0.232 mm.
Explanation:
Power, P = 96 W
Voltage, V = 120 V
Length of wire, l = 4.2 m
Let r be the radius of the wire.
Resistivity of nichrome, ρ = 1.5 x 10^-6 ohm metre
P = V^2 / R
R = 120 x 120 / 96 = 150 ohm
[tex]R = \rho \frac{l}{A}=\rho \frac{l}{\pi r^{2}}[/tex]
[tex]r^2= \rho \frac{l}{\pi \times R}[/tex]
[tex]r^2= \1.5\times10^{-6} \frac{4.2}{3.14 \times 150}[/tex]
r = 1.16 x 10^-4 m
Diameter = 2 x r = 2 x 1.16 x 10^-4 = 2.32 x 10^-4 m = 0.232 mm
Thus, the diameter of the wire is 0.232 mm.
The diameter of the wire is mathematically given as
d=0.232 mm.
Question Parameter(s):
A fish-tank heater is rated at 96 W when connected to 120 V. T
the wire has a total length of 4.2 m
Generally, the equation for the Power is mathematically given as
P = V^2 / R
Where
Resistivity of nichrome, p = 1.5 x 10^-6 ohm m
and
R = (120 x 120) / 96
R= 150 ohm
Therefore
R =p *l/(\pir^2)
r^2= 1.5*10^{-6} 4.2/3.14 *150
r = 1.16 x 10^-4 m
In conclusion, The diameter is
d=2r
d=0.232 mm.
Read more about diameter
https://brainly.com/question/17692316
