The total power dissipated in Watts in the circuit shown here is

Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them by a battery. Then the current per unit length of the cylinder flowing from one cylinder to the other is -

The ammeter $A$ reads $2\, A$ and the voltmeter $V$ reads $20\, V$. The value of resistance $R$ is (Assuming finite resistances of ammeter and voltmeter).

$A$ wire when connected to $220\,V$ mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2$. Then $P_2:P_1$ is

The resistance between points $A$ and $B$ is

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