In an electrical circuit,a battery is connected to pass $20\, C$ of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at $15\, V$. The work done by the battery is ........... $J$.

$A$ circular wire has a current density $J = (2 \times 10^{10} \text{ A/m}^2) r^2$, where $r$ is the radial distance from the center and the wire radius is $2 \text{ mm}$. The potential difference applied across the wire is $50 \text{ V}$. How much energy (in Joules) is converted to thermal energy in $100 \text{ s}$ (in $\pi$)?

If voltage across a bulb rated $220 \,V, 100 \,W$ drops by $2.5 \%$ of its rated value, then the percentage of the rated value by which the power would decrease is (in $\%$)

What is the ratio of heat generated in resistors $R$ and $2R$ connected in parallel as shown in the figure?

$A$ $500\, W$ heating unit is designed to operate from a $115\, V$ line. If the line voltage drops to $110\, V$,the percentage drop in heat output will be ............... $\%$

$A$ total charge $Q$ flows across a resistor $R$ during a time interval $T$ in such a way that the current vs. time graph for $0 \rightarrow T$ is like the loop of a sine curve in the range $0 \rightarrow \pi$. The total heat generated in the resistor is