Two batteries of e.m.f. $4\,V$ and $8\,V$ with internal resistances $1\,\Omega$ and $2\,\Omega$ are connected in a circuit with a resistance of $9\,\Omega$ as shown in the figure. The current and potential difference between the points $P$ and $Q$ are

$A$ heater coil is cut into two equal parts and only one part is used in the heater. What is the ratio of the heat produced by the half coil to that produced by the original full coil?

In the circuit shown,$n$-identical resistors $R$ are connected in parallel $(n > 1)$ and the combination is connected in series to another resistor $R_0$. In the adjoining circuit,$n$ resistors of resistance $R$ are all connected in series along with $R_0$. The batteries in both circuits are identical and the net power dissipated in the $n$ resistors in both circuits is the same. The ratio $R_0 / R$ is

$A$ 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 ammeter in the given circuit reads $2\, A$,the resistance $R$ is ............ $\Omega$.

$A$ potential divider circuit is shown in the figure. The output voltage $V_0$ is