$A$ circuit consists of five identical conductors,each of resistance $1 \ \Omega$,as shown in the figure. Two similar conductors are added as indicated by the dotted lines. The ratio of the equivalent resistances before and after the addition is:

Three identical resistances $A$,$B$,and $C$ are connected as shown in the given figure. The heat produced will be maximum in:

Find the net resistance between points $X$ and $Y$ for the given infinite ladder network,where each resistor has a resistance of $R$.

What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \; mm$ diameter, connected in parallel, gives an equivalent resistance of $3 \; \Omega$? (Given: resistivities of iron and copper-nickel alloy wire are $12 \; \mu\Omega \cdot cm$ and $51 \; \mu\Omega \cdot cm$ respectively) (in $m$)

$(a)$ Three resistors $2 \; \Omega$,$4 \; \Omega$,and $5 \; \Omega$ are combined in parallel. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 20 \; V$ and negligible internal resistance,determine the current through each resistor,and the total current drawn from the battery.

The figure shows a tetrahedron where each edge has a resistance $r$. Choose the correct statement$(s)$ related to the equivalent resistance between any two vertices.