$A$ current of $6\, A$ enters at corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2 \,\Omega$ each and leaves by the corner $R$. The current $i_{1}$ in ampere is ........ .

In the following circuit composed of identical resistors,across which terminals would you connect a battery in order to dissipate energy in all resistors?

Find the potential difference between points $A$ and $B$ in the following circuit. (in $V$)

In the given figure,the equivalent resistance between the points $A$ and $B$ is ............ $\Omega$.

Inside a superconducting ring,six identical resistors each of resistance $R$ are connected as shown in the figure. The equivalent resistance$(s)$:

One end of a Nichrome wire of length $2L$ and cross-sectional area $A$ is attached to an end of another Nichrome wire of length $L$ and cross-sectional area $2A$. If the free end of the longer wire is at an electric potential of $8.0\,V$,and the free end of the shorter wire is at an electric potential of $1.0\,V$,the potential at the junction of the two wires is equal to ............. $V$.