Find the equivalent resistance between the points $a$ and $b$ in $\Omega$.

$A$ current of $15\,mA$ flows in the circuit as shown in the figure. The value of the potential difference between the points $A$ and $B$ will be $...\,V$.

$A$ wire is bent in the form of a circle of radius $2 \ m$. The resistance per unit length of the wire is $\frac{1}{\pi} \ \Omega/m$. $A$ battery of $6 \ V$ is connected between points $A$ and $B$ as shown in the figure. Given $\angle AOB = 90^{\circ}$,find the current flowing through the battery. (in $A$)

The figure shows three resistor configurations $R_1, R_2$, and $R_3$ connected to a $3 \text{ V}$ battery. If the power dissipated by the configurations $R_1, R_2$, and $R_3$ is $P_1, P_2$, and $P_3$ respectively, then:

In the arrangement of resistances shown below,the effective resistance between points $A$ and $B$ is ............... $\Omega$.

If in the circuit,power dissipation is $150\, W$,then $R$ is ............... $\Omega$.