Question

calculate the area of cross section of a wire it's length is 1.0m it's resistance is23ohm and the restivity of the material of a wire is 1.84×10^-6 ohm m
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Answer 1

Given :

• Length of wire, L = 1.0 m
• Resistance of wire, R = 23 Ω
• Resistivity of wire, ρ = 1.84 × 10⁻⁶ Ω m

To find :

• Area of cross section of wire, A = ?

Formula required :

• Relation between Resistance (R), Resistivity (ρ), Length (L) and area of cross section (A)

       R = ρ L / A

[ Where R is in ohms, ρ is in ohm-metres, L in metres and Area in square metres ]

Solution :

Using relation

→ R = ρ L / A

→ 23 = ( 1.84 × 10⁻⁶) ( 1 ) / A

→ 23 = 1.84 × 10⁻⁶ / A

→ A = 1.84 × 10⁻⁶ / 23

→ A = 0.08 × 10⁻⁶  m²

Therefore,

• Area of cross section of wire would be 0.08 × 10⁻⁶  m².

Answer 2

$\tt {\pink{Given}}\begin{cases} \sf{\green{Resistivity=1.84\times 10^{-6}}}\\ \sf{\blue{Length=1 \: m}}\\ \sf{\orange{Resisiatnce=23 \: \Omega}}\\ \sf{\red{Cross \: section \: area= \: ?}}\end{cases}$

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Solution :

$:\implies \sf Resistance = Resistivity \times \dfrac{Length}{Cross \: section \: area}$

$:\implies \sf 23 \: \Omega= 1.84 \times {10}^{ - 6} \times \Bigg \lgroup\dfrac{1}{Cross \: section \: area} \Bigg \rgroup$

$:\implies \sf 23 \: \Omega= \dfrac{1.84 \times {10}^{ - 6}}{Cross \: section \: area}$

$:\implies \sf Cross \: section \: area = \dfrac{1.84 \times {10}^{ - 6} }{23}$

$:\implies \sf Cross \: section \: area = 0.08 \times {10}^{ - 6}$

$:\implies \underline{ \boxed{\textsf{ \textbf {Cross section area = 8 \times {10} ^{ - 8} {m} ^{2} }}}}$

$\therefore\underline{\textsf{The area of Cross section of wire is \textbf{8 \times {10} ^{-8} m ^{2} }}}.$