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

The battery in the diagram is to be charged by the generator $G$. The generator has a terminal voltage of $120 \ V$ when the charging current is $10 \ A$. The battery has an $emf$ of $100 \ V$ and an internal resistance of $1 \ \Omega$. In order to charge the battery at $10 \ A$ charging current,the resistance $R$ should be set at ................ $\Omega$.

$A$ uniform metallic wire carries a current of $2\,A$ when a $3.4\,V$ battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{-3}\,kg$,its density is $8.92 \times 10^3\,kg/m^3$,and its resistivity is $1.7 \times 10^{-8}\,\Omega\cdot m$. The length of the wire is $l = \dots\dots\dots\dots\,m$.

If the galvanometer reading is zero,then the resistance $X = \dots \Omega$.

$A$ fuse wire of radius $0.2 \,mm$ blows off with a current of $5 \,A$. The fuse wire of the same material but of radius $0.3 \,mm$ will blow off with a current of:

$A$ new flashlight cell of $e.m.f.$ $1.5\, V$ gives a current of $15\, A$,when connected directly to an ammeter of resistance $0.04\,\Omega$. The internal resistance of the cell is ........... $\Omega$.