By which of the following single load resistance should the load bridge be replaced so that the power to the load remains unchanged (in $\Omega$)? (Given $r = 3 \ \Omega$ for each resistor in the bridge)

The equivalent resistance between points $A$ and $B$ in the given network is ............ $\Omega$.

Two resistors of resistances $2 \Omega$ and $6 \Omega$ are connected in parallel. This combination is then connected to a battery of emf $2 \text{ V}$ and internal resistance $0.5 \Omega$. What is the current flowing through the battery?

$A$ ring is made of a wire having a total resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{l_1}{l_2}$ of the two segments of the ring between points $A$ and $B$,as shown in the figure,such that the equivalent resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3}\,\Omega$.

What is the equivalent resistance across $A$ and $B$ in the figure shown,if $R = 3\,\Omega$?

Six resistances each of value $r = 6\,\Omega$ are connected between points $A, B$ and $C$ as shown in the figure. If $R_1, R_2$ and $R_3$ are the net resistance between $A$ and $B$,between $B$ and $C$,and between $A$ and $C$ respectively,then $R_1 : R_2 : R_3$ will be equal to: