Heating Effect Questions

An electric kettle takes $4\text{A}$ current at $220\text{V}$. How much time will it take to boil $1\text{kg}$ of water from temperature $20^{\circ }\text{C}$? The temperature of boiling water is $100^{\circ }\text{C}$.

The charge flowing through a resistance $R$ varies with time $t$ as $Q=at-b{t}^2$ where $a$ and $b$ are positive constants. The total heat produced in $R$ is:

A filament bulb $(500\text{W},100\text{V})$ is to be used in a $230\text{V}$ main supply. When a resistance $R$ is connected in series, the bulb works perfectly and consumes $500\text{W}$. The value of $R$ is: