The power consumed when $10 \ V$ voltage is applied to a series combination of $10$ resistors of each $1 \ \Omega$ is $P_{s}$ and the power consumed when the same $10 \ V$ is applied to the parallel combination of these $10$ resistors is $P_p$. The value of $\frac{P_{s}}{P_{p}}$ is

$A$ uniform metallic wire has a resistance of $18\,\Omega$ and is bent into an equilateral triangle. Then,the resistance between any two vertices of the triangle is .................. $\Omega$.

$10$ resistors,each of resistance $R$,are connected in series to a battery of $emf$ $E$ and negligible internal resistance. When those are connected in parallel to the same battery,the current is increased $n$ times. The value of $n$ is:

Consider two circuits, $(A)$ and $(B)$, each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient of resistance, $-\alpha$. The current through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

$A$ wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of the equivalent resistance between the two end points of an edge of the triangle to that of the square is