$A$ railway compartment is lit up by thirteen lamps,each taking $2.1\,A$ at $15\,V$. The heat generated per second in each lamp will be ............ $cal$.

Why is electric power transmitted at very high voltage over long distances to reduce Ohmic loss?

$A$ coil develops heat of $800 \, cal/sec$ when $20 \, V$ is applied across its ends. The resistance of the coil is .............. $\Omega$ $(1 \, cal = 4.2 \, J)$.

There are $n$ number of identical electric bulbs,each designed to draw a power $P$ independently from the mains supply. If they are now joined in series across the same mains supply,what is the total power drawn by the combination?

If the power in the external resistance $R$ is maximum,then which of the following statements are correct?
$(i) R = r$
$(ii)$ Power in $R$ is $\frac{E^2}{4R}$
$(iii)$ Input power is $\frac{E^2}{2R}$
$(iv)$ Efficiency is $50\%$

When the power delivered by a $100\,V$ battery is $40\,W$,the equivalent resistance of the circuit is ........... $\Omega$.