$A$ uniform wire of resistance $4 \ \Omega$ is bent into the shape of a semicircle. What is the equivalent resistance between the two ends of the diameter (in $\Omega$)?

$A$ uniform ring of conducting wire of radius $r$ has resistance $R$. $A$ and $B$ are two points on the ring which subtend an angle $\theta$ at the centre of the ring. The equivalent resistance between points $A$ and $B$ is:

Two bulbs $X$ and $Y$ having the same voltage rating and power ratings of $40\, W$ and $60\, W$ respectively are connected in series across a potential difference of $300\, V$. Then:

The resistance of the series combination of two identical resistors is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is

The equivalent resistance of a group of resistances is $R$. If another resistance is connected in parallel to the group,its new equivalent becomes $R_1$,and if it is connected in series to the group,its new equivalent becomes $R_2$. We have:

The equivalent resistance of resistors connected in series is always