Heat is produced at a rate given by $H$ in a resistor when it is connected across a supply of voltage $V$. If now the resistance of the resistor is doubled and the supply voltage is made $V / 3$, then the rate of production of heat in the resistor will be

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

$A$ $6.0\,V$ battery is connected to two light bulbs as shown in the figure. Light bulb $1$ has a resistance of $3\,\Omega$ while light bulb $2$ has a resistance of $6\,\Omega$. The battery has negligible internal resistance. Which bulb will glow brighter?

$A$ $5\,^{\circ}\text{C}$ rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately ........... $^{\circ}\text{C}$

Four wires of the same diameter are connected in turn between two points,maintained at a constant potential difference. Their resistivities and lengths are: $\rho$ and $L$ (wire $1$),$1.2\rho$ and $1.2L$ (wire $2$),$0.9\rho$ and $0.9L$ (wire $3$),and $\rho$ and $1.5L$ (wire $4$). Rank the wires according to the rates at which energy is dissipated as heat,greatest first.

An electric heater rated $220 \,V$ and $550 \,W$ is connected to $AC$ mains. The current drawn by it is (in $\,A$)