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Six resistors of $3 \;\Omega$ each are connected along the sides of a hexagon and three resistors of $6\; \Omega$ each are connected along $A C, A D$ and $A E$ as shown in the figure. The equivalent resistance between $A$ and $B$ is equal to
$n$ identical cells are joined in series with two cells $A$ and $B$ with reversed polarities. $emf$ of each cell is $E$ and internal resistance is $r$. Potential difference across cell $A$ and $B$ is : $(n > 4)$
Current density in a cylindrical wire of radius $R$ is given as $J =$ $\left\{ {\begin{array}{*{20}{c}}
{{J_0}\left( {\frac{x}{R} - 1} \right)\,\,for\,\,0 \leqslant x < \frac{R}{2}} \\
{{J_0}\frac{x}{R}\,\,\,\,for\,\,\,\frac{R}{2} \leqslant x \leqslant R}
\end{array}} \right.$The current flowing in the wire is:
A wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is mid-point of arm $CD$ )