CBSE Class 10 Science Exam 2014 Term 1 Paper

Question : 15 of 36

Marks: +1, -0

The resistance of a wire of

0.01 {\cm}

radius is

10 Ω

. If the resistivity of the material of the wire is

50 × 10^{-8} {\ohm}

metre, find the length of the wire.

Solution:

Given : Resistance of a wire,

R=10 Ω

Radius of wire,

r=0.01 {\cm}=0.01 × 10^{-2} {\m}

Resistivity,

ρ=50 × 10^{-8} Ω {\m}

Area of cross-section of wire A,

=π r^2=3.14 × (0.01 × 10^{-2}) ^2

=3.14 × 0.01 × 0.01 × 10^{-4}

=3.14 × 10^{-8} {\m}^2

As,

{\R}\;=ρ \;{l}/{ {\A}}

l\;=\;{ {\R} × {\A}}/{ρ}=\;{10 × 3.14 × 10^{-8}}/{50 × 10^{-8}}

\;=0.628 {\m}

l\;=\;{ {\R} × {\A}}/{ρ}=\;{10 × 3.14 × 10^{-8}}/{50 × 10^{-8}}

\;=0.628 {\m}

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