Question

A wire of radius 0.4 to mm and resistivity 44 into 10 power minus 8 ohm metre is available in a laboratory calculate the length of a wire needed to have a resistance of 15 ohm

Answer 1

Explanation:

•radius (r)=0.4mm

1mm=0.001m

0.4mm=0.001*0.4=0.0004m

•area=πr^2

=3.14*0.0004*0.0004

=5024*10^-10

•resitivity(P)=44*10^-8ohm m

•resistance(r)=15ohm

•length=?

we know that P= R*A/l

l=R*A/P

l=15*5024*10^-10/44*10^-8

l=17.1272m

for full calculation refer to the atatchment

Answer 2

radius (r) = 0.4 mm

=> 0.0004 m

Resistivity $(\rho)$ = 44 × ${10}^{-8}$ ohm m

Resistance (R) = 15 ohm

_________ [ GIVEN ]

• We have to calculate the length (l) of the wire.

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We know that..

$R \: = \: \rho \: \dfrac{l}{A}$

Here ..

A is Area. And we know that area = π r²

Area = $\frac{22}{7}$ × (0.0004)²

=> 31.4 × 0.00000016

=> 50.24 × ${10}^{-8}$

=> 5.024 × ${10}^{-9}$

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Now..

$R \: = \: \rho \: \dfrac{l}{A}$

$l\:=\:\dfrac{RA}{ \rho}$

=> l = $\dfrac{15 \: \times \: 5.024 \: \times {10}^{ - 9} }{44 \: \times \: {10}^{ - 8} }$

=> l = $\dfrac{75.36\times {10}^{ - 9 \: + 8 \: = \: - 1} }{44 }$

=> l = 1.71273 × 10-¹ m

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Length of the wire is 1.71273 × 10-¹ m

___________ [ ANSWER ]

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