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

The effective resistance of two resistors in parallel is $\frac{12}{7} \ \Omega$. If one of the resistors is disconnected,the resistance becomes $4 \ \Omega$. The resistance of the other resistor is ............. $\Omega$.

Two $10\,\Omega$ resistors are first connected in series and then in parallel. What is the ratio of the equivalent resistance in both cases?

$A$ and $B$ are two points on a uniform ring of radius $r$. The resistance of the ring is $R$. $\angle AOB = \theta$ as shown in the figure. The equivalent resistance between points $A$ and $B$ is . . . . . . .

When two resistors of $R \ \Omega$ value are connected in parallel,what is the equivalent resistance?

Two bulbs are connected in parallel. Bulb $A$ is brighter than bulb $B$. If $R_A$ and $R_B$ are their resistances respectively,then: