(D) The resistance $R$ of a conductor is given by $R = \rho \frac{l}{A}$.Here,the cross-sectional area $A$ is the area of the hollow part: $A = \pi (r

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(D) The resistance $R$ of a conductor is given by $R = \rho \frac{l}{A}$.Here,the cross-sectional area $A$ is the area of the hollow part: $A = \pi (r_2^2 - r_1^2)$.Given: $r_2 = 10 \, cm = 0.1 \, m$,thickness $t = 5 \, mm = 0.005 \, m$.So,inner radius $r_1 = r_2 - t = 10 \, cm - 0.5 \, cm = 9.5 \, cm = 0.095 \, m$.$A = \pi [(0.1)^2 - (0.095)^2] = \pi [0.01 - 0.009025] = \pi [0.000975] \, m^2$.Now,$R = (1.7 \times 10^{-8}) \times \frac{5}{\pi \times 0.000975} \approx 2.77 \times 10^{-5} \, \Omega$.

Class 12 Physics Current Electricity Resistance of wire, Resistivity and Conductivity

Difficult

What is the resistance of a wire of length $5 \, m$ and resistivity $1.7 \times 10^{-8} \, \Omega \cdot m$,given the cross-sectional area is a hollow cylinder with outer radius $r_2 = 10 \, cm$ and thickness $5 \, mm$?

A
$5.6 \times 10^{-5} \, \Omega$
B
$2 \times 10^{-5} \, \Omega$
C
$4 \times 10^{-5} \, \Omega$
D
None of these

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Current Electricity

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Resistance of wire, Resistivity and Conductivity

Given below are two statements:
Statement $I$: The resistivity of a conductor is independent of its temperature.
Statement $II$: The resistivity of a semiconductor decreases with an increase in temperature.
Select the correct option.

MediumKCET 2026

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$A$ piece of copper is to be shaped into a conducting wire of maximum resistance. If the initial length is $L$ and diameter is $d$,what should be the new length and diameter to achieve maximum resistance?

DifficultKCET 2017

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With an increase in temperature,the resistivity of a conductor ........ and the resistivity of a semiconductor ....... .

Easy

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The length of a given cylindrical wire is increased by $100 \%$. Due to the consequent decrease in diameter, the change in the resistance of the wire will be .................. $\%$

MediumAIEEE 2003

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The resistance of a conductor at $20\,^{\circ}C$ and $500\,^{\circ}C$ is $20\,\Omega$ and $60\,\Omega$ respectively. At what temperature will the resistance be $25\,\Omega$?

Medium

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What is the resistance of a wire of length $5 \, m$ and resistivity $1.7 \times 10^{-8} \, \Omega \cdot m$,given the cross-sectional area is a hollow cylinder with outer radius $r_2 = 10 \, cm$ and thickness $5 \, mm$?

Similar Questions

Given below are two statements:Statement $I$: The resistivity of a conductor is independent of its temperature.Statement $II$: The resistivity of a semiconductor decreases with an increase in temperature.Select the correct option.

$A$ piece of copper is to be shaped into a conducting wire of maximum resistance. If the initial length is $L$ and diameter is $d$,what should be the new length and diameter to achieve maximum resistance?

With an increase in temperature,the resistivity of a conductor ........ and the resistivity of a semiconductor ....... .

The length of a given cylindrical wire is increased by $100 \%$. Due to the consequent decrease in diameter, the change in the resistance of the wire will be .................. $\%$

The resistance of a conductor at $20\,^{\circ}C$ and $500\,^{\circ}C$ is $20\,\Omega$ and $60\,\Omega$ respectively. At what temperature will the resistance be $25\,\Omega$?

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Given below are two statements:
Statement $I$: The resistivity of a conductor is independent of its temperature.
Statement $II$: The resistivity of a semiconductor decreases with an increase in temperature.
Select the correct option.