$A$ current of $3 \, A$ flows through the $2 \, \Omega$ resistor shown in the circuit. The power dissipated in the $5 \, \Omega$ resistor is ................. $W$.

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:

What is the equivalent resistance between $P$ and $Q$ in the given circuit?

Four wires $AB, BC, CD, DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$,where $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is:

Two wires of the same material and equal length are joined in parallel combination. If one of them has half the thickness of the other and the thinner wire has a resistance of $8\, \Omega$,the resistance of the combination is equal to

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