In the network of resistors shown in the adjoining figure,the equivalent resistance between $A$ and $B$ is ............ $ohm$.

In the circuit shown in the figure,switch $S_1$ is initially closed and $S_2$ is open. Find $V_a - V_b$ in $V$.

In the circuit shown in the figure,all cells are ideal. The current through the $2 \, \Omega$ resistor is ............ $A$.

An ammeter and a voltmeter of resistance $R$ are connected in series to an electric cell of negligible internal resistance. Their readings are $A$ and $V$ respectively. If another resistance $R$ is connected in parallel with the voltmeter, what happens to the readings $A$ and $V$?

An electric kettle has two heating coils. When the first coil is switched on, the tea boils in $6$ minutes. When the second coil is switched on, it boils in $8$ minutes. If both coils are connected in series and switched on, how long will it take for the tea to boil?

Two wires $A$ and $B$ made of the same material and having their lengths in the ratio $6 : 1$ are connected in series. The potential differences across the wires are $3\,V$ and $2\,V$ respectively. If $r_A$ and $r_B$ are the radii of $A$ and $B$ respectively,then $\frac{r_B}{r_A}$ is