Question

The figure below shows three cylindrical copper conductors along with their face areas and lengths compare the resistance and the resistivity of the three conductors justify your answer

Answer 1

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

# First Cylinder (a)

• Length = L
• Area = A

$\Large{\sf{R \: = \: \rho \: \frac{L}{A}}---(1)}$

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# Second Cylinder (b)

• Length = 3L
• Area = A/3

Put Value in (1)

$\Large \leadsto {\sf{R' \: = \: \rho \: \frac{3L}{\frac{A}{3}}}}$

$\Large \leadsto {\sf{R' \: = \: \rho \: (\frac{9L}{A})}}$

$\LARGE \implies {\sf{R' \: = \: 9R}}$

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# 3rd Cylinder (c)

• Area = 3A
• Length = L/3

Put Value in (1)

$\Large \leadsto {\sf{R" \: = \: \rho \: \frac{L}{3(3A)}}}$

$\Large \leadsto {\sf{R" \: = \: \frac{1}{9} \: \rho \: (\frac{L}{A})}}$

$\LARGE \implies {\sf{R" \: = \: \frac{1}{9} \: R}}$

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Comparing according to resistance

R' > R > R"