The resistance of the filament of a lamp increases with the increase in temperature. $A$ lamp rated $100\, W, 220\, V$ is connected across a $220\, V$ power supply. If the voltage drops by $10\%$,then the power of the lamp will be:

$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current,the temperature of the wire is raised by $\Delta T$ in a time $t$. $A$ number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is

$A$ $100 \ W$ bulb is rated at $200 \ V$ and a $200 \ W$ bulb is rated at $100 \ V$. Then:

Match the following two columns:

Column-$I$	Column-$II$
$(A)$ Electrical resistance	$(P)$ $M^1 L^3 T^{-3} A^{-2}$
$(B)$ Electrical potential	$(Q)$ $M^1 L^2 T^{-3} A^{-2}$
$(C)$ Specific resistance	$(R)$ $M^1 L^2 T^{-3} A^{-1}$
$(D)$ Specific conductance	$(S)$ None of these

In a silver voltameter, $2.89 \ g$ of silver is deposited in $10 \ minutes$. The heat produced in a $20 \ \Omega$ resistor for the same time will be ................ $kJ$.

$A$ conductor is made of an isotropic material and has the shape of a truncated cone. $A$ battery of constant emf is connected across it and its left end is earthed as shown in the figure. If at a section distant $x$ from the left end, electric field intensity, potential, and the rate of generation of heat per unit length are $E, V$, and $H$ respectively, which of the following graphs is/are correct?