A copper transmission cable 170 km long and 10.0 cm in diameter carries a current of 100 A .
1 answer:
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Answer:
The percentage change in resistance of the wire is 69%.
Explanation:
Resistance of a wire can be determined by,
R = (ρl) ÷ A
Where R is its resistance, l is the length of the wire, A its cross sectional area and ρ its resistivity.
When the wire is stretched, its length and area changes but its volume and resistivity remains constant.
= 1.3l, and
=
So that;
= (ρ
) ÷
= (ρ × 1.3l) ÷ (
)
= (1.3lρ) ÷ ()
= × [(ρl) ÷ A]
= 1.69R (∵ R = (ρl) ÷ A)
= 1.69R
Where is the new resistance,
is the new length, and
is the new area after stretching the wire.
The change in resistance of the wire = - R
= 1.69R - 1R
= 0.69R
The percentage change in resistance = × 100
= 0.69 × 100
= 69%
The percentage change in resistance of the wire is 69%.
Answer:
<em>radius of the loop = 7.9 mm</em>
<em>number of turns N ≅ 399 turns</em>
Explanation:
length of wire L= 2 m
field strength B = 3 mT = 0.003 T
current I = 12 A
recall that field strength B = μnI
where n is the turn per unit length
vacuum permeability μ = = 1.256 x 10^-6 T-m/A
imputing values, we have
0.003 = 1.256 x 10^−6 x n x 12
0.003 = 1.507 x 10^-5 x n
n = 199.07 turns per unit length
for a length of 2 m,
number of loop N = 2 x 199.07 = 398.14 ≅ <em>399 turns</em>
since there are approximately 399 turns formed by the 2 m length of wire, it means that each loop is formed by 2/399 = 0.005 m of the wire.
this length is also equal to the circumference of each loop
the circumference of each loop =
0.005 = 2 x 3.142 x r
r = 0.005/6.284 = = 0.0079 m =<em> 7.9 mm</em>