$A$ ($100\, W$,$200\, V$) bulb is connected to a $160\, V$ power supply. The power consumption would be ............. $W$.

The resistance of an electrical toaster has a temperature dependence given by $R(T) = R_0[1 + \alpha(T - T_0)]$ in its range of operation. At $T_0 = 300\,K, R = 100\,\Omega$ and at $T = 500\,K, R = 120\,\Omega$. The toaster is connected to a voltage source of $200\,V$ and its temperature is raised at a constant rate from $300\,K$ to $500\,K$ in $30\,s$. The total work done in raising the temperature is:

$A$ $220\, V$,$1000\, W$ bulb is connected across a $110\, V$ mains supply. The power consumed will be ............ $W$.

Assertion: Long distance power transmission is done at high voltage.
Reason: At high voltage supply,power losses are less.

$A$ piece of fuse wire melts when a current of $15\, A$ flows through it. With this current,if it dissipates $22.5\, W$,the resistance of the fuse wire will be .............. $\Omega$.

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 $50\%$