$A$ battery with $EMF$ $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when:

Two electric bulbs have resistances in the ratio $1 : 2$. If they are connected in parallel to a constant voltage source,the ratio of power dissipated in them will be:

$A$ heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

$A$ 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 ............ $cal$.

The resistance of a device component decreases as the current through it increases and it is described by the relation,$R = \frac{0.2 I}{I-4}$,where $I$ is the current. Determine the minimum power delivered. (Assume $I > 4$) (in $W$)

Power generated across a uniform wire connected across a supply is $H$. If the wire is cut into $n$ equal parts and all the parts are connected in parallel across the same supply,the total power generated in the wire is