Two bulbs,one of $50\, W$ and another of $25\, W$,are connected in series to the mains. The ratio of the currents through them is:

In the given circuit,all resistances are of value $R \ \Omega$ each. The equivalent resistance between $A$ and $B$ is:

When two conducting wires are connected in series,the equivalent resistance is $14\, \Omega$,and when they are connected in parallel,the equivalent resistance is $3.43\, \Omega$. The resistance of the wire with the higher value is ................. $\Omega$.

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:

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

$A$ wire has a resistance of $6 \,\Omega$. It is cut into two equal parts and both parts are connected in parallel. The new resistance is ................ $\Omega$.