The power dissipated in the circuit shown in the figure is $30 \, W$. The value of $R$ is ............. $\Omega$.

First,a set of $n$ equal resistors of $R$ each are connected in series to a battery of $emf$ $E$ and internal resistance $R$. $A$ current $I$ is observed to flow. Then,the $n$ resistors are connected in parallel to the same battery. It is observed that the current increases $10$ times. What is $n$?

Consider the following two circuits:
$A$: $20$ bulbs are connected in series to a power supply line.
$B$: $20$ bulbs identical to $A$ are connected in a parallel circuit to an identical power supply line.
Identify which of the following is not true.

Five identical electric filament lamps numbered $1$ to $5$ are joined in parallel across an ideal source as shown in the figure. When all the bulbs are working, the reading in the ammeter is $3 \,A$. When lamp '$1$' is switched off, the reading of the ammeter is (in $\,A$)

Given three equal resistors,how many different combinations of all the three resistors can be made?

$A$ uniform ring of conducting wire of radius $r$ has resistance $R$. $A$ and $B$ are two points on the ring which subtend an angle $\theta$ at the centre of the ring. The equivalent resistance between points $A$ and $B$ is: