Two electric bulbs marked $40\,W, 220\,V$ and $60\,W, 220\,V$ are connected in series across a $220\,V$ supply,resulting in an effective power $P_1$. When they are connected in parallel across the same $220\,V$ supply,the effective power is $P_2$. The ratio $\frac{P_1}{P_2}$ is:

Amount of electricity required to pass through the ${H_2O}$ voltmeter so as to liberate $11.2 \, L$ of hydrogen will be ............ $F$.

The two ends of a uniform conductor are joined to a cell of $e.m.f.$ $E$ and some internal resistance. Starting from the midpoint $P$ of the conductor,we move in the direction of current and return to $P$. The potential $V$ at every point on the path is plotted against the distance covered $(x)$. Which of the following graphs best represents the resulting curve?

For a given thermocouple,the thermo $e.m.f.$ can be

Answer the following questions:
$(a)$ $A$ steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?
$(b)$ Is Ohm's law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm's law.
$(c)$ $A$ low voltage supply from which one needs high currents must have very low internal resistance. Why?
$(d)$ $A$ high tension $(HT)$ supply of, say, $6 \ kV$ must have a very large internal resistance. Why?

In the circuit shown in the figure,find the current through the $4\,\Omega$ resistor.