In the following circuit, $1 \,\Omega$ resistor dissipates power $P$. If the resistor is replaced by $9 \,\Omega$, the power dissipated in it is
$P$
$3 P$
$9 P$
$\frac{P}{3}$
The electric current passing through a metallic wire produces heat because of
A heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils)
A $220 \; V , 50 \; Hz$ AC source is connected to a $25 \; V$, $5 \; W$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be
If the length of the filament of a heater is reduced by $10\%$, the power of the heater will
A current i passes through a wire of length $l$, radius of cross-section $r$ and resistivity $\rho$. The rate of heat generation is