Question

A metal wire of specific resistance 64×10^-6ohm cm and the length 198cm has a resistance of 7ohm the radius of the wire is

Answer 1

radius is equal to root of 64 into 10 raise to power minus 6 into 198 / 7pi

Answer 2

➠Question:-

A metal wine of specific resistivity 64x 10 -⁶ ohm cm and long the 1.98 cm has a resistance of 7ohm.The radius of wire is___

➠Given:-

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$\sf \red \bigstar\rho \: _{metal \: wire} = 64 \times 10^{ - 6} ohm \: cm$

$\green \bigstar \sf \: length \: (l) _{metal \: wire} = 198 \: cm \:$

$\purple \bigstar \sf resistance \: _{metal \: wire} = 7 \Omega$

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➠To find out:-

$\sf \leadsto\: radius \: of \: the \: metal \: wire = {?}$

➠Solution:-

As we know that

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$\bigstar \underline{ \boxed{ \sf \red{R = \dfrac{ \rho \: l}{A}}} }$

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$\longrightarrow \sf R = \dfrac{ \rho \: l}{ \pi \: {r}^{2} }$

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$\longrightarrow \sf r = \sqrt{ \dfrac{ \rho \: l}{ \pi \: R} }$

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$\longrightarrow \sf r = \sqrt{ \dfrac{64 \times {10}^{ - 6} \times 198}{3.14\: 7} }$

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$\large \boxed{ \blue{\longrightarrow \sf r = 0.024 \: cm \:} }$

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More to know:-

• Resistivity of a material is defined as resistance offered by a cylinder or a cube of one metre² and one metre when current flows perpendicular to the opposite end of it.

• Resistivity depends on the nature of the material of the conductor and also om Temperature.

• Unit of Resistivity is ohm m or ohm cm.

• Different elements have different Resistivity. Silver has lowest Resistivity 1.6×10-⁸ while nichrome has the highest 100×10-⁸.Thus silver us good conductor of electricity while nichrome is bad conductor of electricity.

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