A Coppen wire has a diameter of 0.5mm and
a resistivity of 1.6 Ohm.cm How much of this wire
would be required to make
10 ohm coil.
Answers
Hey, here's ur answer:
Given:
Diameter = 0.5 mm = 0.5 ×10^{-3}10
−3
Resistivity = 1.6 × 10^{-6}10
−6
Siemens per centimeter
= 1.6 × 10^{-4}10
−4
Siemens per meter
Resistance = 10 Ohm
To find:
Length of wire = ?
Formula used:
Resistance of the wire is given by,
R = ω \frac{l}{A}
A
l
Where R is the resistance
ω = resistivity
A = area of cross section
l = length of wire
Solution:
Area of cross section of a wire = Area of the circle
A = πr^{2}r
2
A = 3.14 × \frac{0.5}{2} \times10^{-3} \times \frac{0.5}{2} \times 10^{-3}
2
0.5
×10
−3
×
2
0.5
×10
−3
A = 1.9625 × 10^{-7}10
−7
Resistance of the wire is given by,
R = ω \frac{l}{A}
A
l
Where R is the resistance
ω = resistivity
A = area of cross section
l = length of wire
l = \frac{RA}{ω}
ω
RA
l = \frac {1.9625 \times 10^{-7} \times 10}{1.6 \times 10^{-4} }
1.6×10
−4
1.9625×10
−7
×10
l = 12.26 ×10^{-3}10
−3
meter
l = 12.26 millimeter
Thus, length of wire required to make 10 Ohm coil is 12.26 mm
Hope it helps
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