Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire

Q: Two uniform wires $A$ and $B$ are of the same metal and have equal masses. The radius of wire $A$ is twice that of wire $B$. The total resistance of A and $B$ when connected in parallel is

a $\frac{{{R_A}}}{{{R_B}}} = {\left( {\frac{{{r_B}}}{{{r_A}}}} \right)^4}$ $ \Rightarrow $ $\frac{{{R_A}}}{{{R_B}}} = {\left( {\frac{1}{2}} \right)^4} = \frac{1}{{16}}$ $ \Rightarrow $ ${R_B} = 16{R_A}$ When $R_A$ and $R_B $ are connected in parallel then equivalent resistance ${R_{eq}} = \frac{{{R_A}{R_B}}}{{({R_A} + {R_B})}} = \frac{{16}}{{17}}{R_A}$ If ${R_A} = 4.25\,\Omega $ then ${R_{eq}} = 4\,\Omega $ i.e. option $(a)$ is correct.

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Two uniform wires $A$ and $B$ are of the same metal and have equal masses. The radius of wire $A$ is twice that of wire $B$. The total resistance of A and $B$ when connected in parallel is

A$4\,\Omega $ when the resistance of wire $A$ is $4.25\,\Omega $
B$5\,\Omega $ when the resistance of wire $A$ is $4.25\,\Omega $
C$4\,\Omega $ when the resistance of wire $B$ is $4.25\,\Omega $
D$4\,\Omega $ when the resistance of wire $B$ is $4.25\,\Omega $

Medium

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

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