An electric lamp is marked $60\, W$, $230\, V$. The cost of $1\, kWh$ of energy is Rs. $1.25$. The cost of using this lamp for $8$ hours a day for $30$ days is Rs. ...............

$A$ constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled,the rate of heat developed in the wire will be

$A$ button battery is rated $3 \,V$ and $225 \,mAh$. $A$ cricket ball (mass $= 0.163 \,kg$) having energy equal to that stored in the battery will have a speed closest to ............ $\,m/s$.

Two bulbs of $250 \ V$ and $100 \ W$ are first connected in series and then in parallel with a supply of $250 \ V$. Total power in each of the cases will be . . . . . . respectively.

The figure shows a thick spherical shell made of a material with electrical conductivity $\sigma$. It has inner and outer radii of $10\ cm$ and $20\ cm$ respectively and is filled with ice inside. Its inner and outer surfaces are kept at different potentials by a battery with internal resistance $r = \frac{2}{\pi}\ \Omega$ and electromotive force $\epsilon = 5\ V$. Find the value of $\sigma$ for which the ice melts at the maximum possible rate,given that $25\%$ of the heat generated by the shell due to Joule heating is used to melt the ice.

The current density in a circular wire is given by $J(r) = (1 \times 10^5 \text{ A/m}^3) r$,where $r$ is the radial distance and the wire's radius is $2 \text{ mm}$. If the potential applied across the wire is $70 \text{ V}$,then the energy consumed by the wire in $1000 \text{ s}$ is: