Two electrical bulbs marked $40\, W, 220\, V$ and $60\, W, 220\, V$ are connected in series across a $220\, V$ supply. The effective power is $P_1$. When they are connected in parallel across the same supply, the effective power is $P_2$. The ratio $(P_1/P_2)$ is:

$A$ wire of resistance $10 \, \Omega$ is bent to form a circle. $P$ and $Q$ are points on the circumference of the circle dividing it into a quadrant and are connected to a battery of $3 \, V$ and internal resistance $1 \, \Omega$ as shown in the figure. The currents in the two parts of the circle are

$A$ uniform metallic wire of length $L$ is mounted in two configurations. In configuration $1$ (triangle),it is an equilateral triangle and a voltage $V$ is applied to corners $A$ and $B$. In configuration $2$ (circle),it is bent in the form of a circle and the potential $V$ is applied at diametrically opposite points $P$ and $Q$. The ratio of the power dissipated in configuration $1$ to configuration $2$ is

Two heating coils, one of fine wire and the other of thick wire of the same material and of the same length, are connected in series and in parallel. Which of the following statements is correct?

$A$ copper voltameter is connected in parallel with a heater coil of resistance $0.1\,\Omega$. $A$ current is passed for $20\,\text{minutes}$,resulting in the deposition of $0.99\,\text{g}$ of copper on the cathode. If the electrochemical equivalent of copper is $0.00033\,\text{g/C}$,the heat produced in the coil is ........... $J$.

Match the List-$I$ with the List-$II$ from the combination shown. In the left side (List-$I$) there are four different conditions and in the right side (List-$II$), there are ratios of heat produced in each resistance for each condition:

List-$I$	List-$II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them	$(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $\Omega$ are connected in series and same $P.D.$ is applied across them	$(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them	$(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1:2$ are connected in parallel and same $P.D.$ is applied across them	$(D)$ $2:1$