A fuse made of lead wire has an area of cross-section $0.3{ \mathrm{mm}}^2$ on short circuiting the current in the fuse wire reaches $30 A$. How long (in milli second) after the short circuiting, Will the fuse begin to melt ?
For lead, specific heat $=0.022{\mathrm{calg}}^{-1}{\left({}^0\mathrm{C}\right)}^{-1}$, melting point $={327}^0\mathrm{C}$, density $=2 \mathrm{g}{ \mathrm{cm}}^{-3}$ and the resistivity $=22\times {10}^{-6}\Omega \mathrm{cm}$. The initial temperature of the wire is ${27}^0\mathrm{C}$ (neglect heat losses)

A resistor dissipates $192 \mathrm{J}$ of energy in $1 \mathrm{s}$ when a current of $4 \mathrm{A}$ is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in $5 \mathrm{s}$ is _____________ $\mathrm{J}.$

$ADC$ source with internal resistance $R_0$ is connected to circuit as shown in the figure. The value of $R$ for which the power generated in the circuit is the maximum is

Two resistors $R_1$and $R_2$ of $4\Omega$ and $6\Omega$  are connected in parallel across a battery. The ratio of power dissipated in them, P1 : P2 will be

A water heater of power $2000 \mathrm{W}$ is used to heat water. The specific heat capacity of water is $4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$. The efficiency of heater is $70\%$. Time required to heat $2 \mathrm{kg}$ of water from $10°\mathrm{C}$ to $60°\mathrm{C}$ is _____ $\mathrm{s}$.

(Assume that the specific heat capacity of water remains constant over the temperature range of the water).