In an electrical cable there is a single wire of radius 9, mm of copper. Its resistance is 5,Omega . The cable is replaced by

Q: In an electrical cable there is a single wire of radius $9\, mm$ of copper. Its resistance is $5\,\Omega $. The cable is replaced by $6$ different insulated copper wires, the radius of each wire is $3\,mm$. Now the total resistance of the cable will be ............... $\Omega$

a (a) Initially : Resistance of given cable $R = \rho \frac{l}{{\pi \times {{(9 \times {{10}^{ - 3}})}^2}}}$ ... $(i)$ Finally : Resistance of each insulated copper wire is $R\,' = \rho \frac{l}{{\pi \times {{(3 \times {{10}^{ - 3}})}^2}}}$. Hence equivalent resistance of cable ${R_{eq}} = \frac{{R\,'}}{6} = \frac{1}{6} \times \left( {\rho \frac{l}{{\pi \times {{(3 \times {{10}^{ - 3}})}^2}}}} \right)$….$(ii)$ On solving equation $(i)$ and $(ii)$ we get $R_{eq} = 7.5 \,\Omega$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

In an electrical cable there is a single wire of radius $9\, mm$ of copper. Its resistance is $5\,\Omega $. The cable is replaced by $6$ different insulated copper wires, the radius of each wire is $3\,mm$. Now the total resistance of the cable will be ............... $\Omega$

A$7.5$
B$45$
C$90$
D$270$

Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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