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
Medium
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$\frac{{{R_A}}}{{{R_B}}} = {\left( {\frac{{{r_B}}}{{{r_A}}}} \right)^4}$ $ \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.
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