$1.0\, m$ લંબાઇ અને $0.6\, cm $ વ્યાસ ધરાવતા તારનો અવરોધ $3.0 \times 10^{-3}\,Ω$ છે.સમાન દ્રવ્યમાંથી બનાવેલ $2.0\, cm $ વ્યાસ અને $1.0\, mm$ જાડાઇ ધરાવતી તકતી વચ્ચેનો અવરોધ કેટલો થાય?

Question

A$1.35 × 10^{-6}\,\Omega$
B$2.7×10^{-7} \,\Omega$
C$4.05 × 10^{-6} \,\Omega$
D$8.1 × 10^{-6}\,\Omega$

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Solution

b
$R = \rho .\frac{l}{A};\frac{{{R_{{\rm{disc}}}}}}{{{R_{{\rm{rod}}}}}} = \frac{{{l_{{\rm{disc}}}}}}{{{l_{{\rm{rod}}}}}} \times \frac{{{A_{{\rm{rod}}}}}}{{{A_{{\rm{disc}}}}}}$ $\Rightarrow $ $\frac{{{R_{{\rm{disc}}}}}}{{3 \times {{10}^{ - 3}}}} = \frac{{{{10}^{ - 3}}}}{1} \times \frac{{\pi {{(0.3 \times {{10}^{ - 2}})}^2}}}{{\pi {{({{10}^{ - 2}})}^2}}}$

$\Rightarrow $ $ R_{disc} = 2.7 ×10^{-7}\,\Omega$ .

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