If you are provided with three resistors of $2 \,\Omega$,$3 \,\Omega$,and $6 \,\Omega$,how will you connect them to obtain an equivalent resistance of $4 \,\Omega$?

Explain the series connection of resistors. Derive the equation for the equivalent resistance $(R_S)$.

$A$ wire of resistance $100 \Omega$ is stretched so that its length increases by $20 \%$. The stretched wire is then bent in the form of a rectangle whose length and breadth are in the ratio $3: 2$. The effective resistance between the ends of any diagonal of the rectangle is (in $\Omega$)

The equivalent resistance of three unequal resistors connected in parallel is $1 \ \Omega$. If the ratio of two of them is $1:2$ and all resistance values are integers,what is the value of the largest resistor in ohms?

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 $m$)

Obtain the expression for the equivalent resistance for $3$ resistors connected in parallel and also write the expression of equivalent resistance for connection of $n$ resistors.