$A$ potential divider is used to give outputs of $4\, V$ and $8\, V$ from a $12\, V$ source. Which combination of resistances $(R_1, R_2, R_3)$ gives the correct voltages? Find the ratio $R_1 : R_2 : R_3$.

The potential difference between the points $P$ and $Q$ in the electric circuit shown is ................. $V$.

$A$ cell sends a current of $0.9\, A$ through a resistance of $2\, \Omega$ and a current of $0.3\, A$ through a resistance of $7\, \Omega$. The internal resistance of the cell is ............. $\Omega$.

When the terminals of a cell are connected by a wire of resistance $4 \Omega$,the potential difference across the cell is $1.6 \text{ V}$. If a wire of the same resistance is connected in parallel with the first,the potential difference becomes $1.33 \text{ V}$. The emf and internal resistance of the cell are respectively

$A$ 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 $l = \dots\dots\dots\dots\,m$.

Calculate the current shown by the ammeter $A$ in the circuit diagram. (in $A$)