An expression for rate of heat generated, if a current of $I$ ampere flows through a resistance of $R$ $\Omega$, is

The same mass of copper is drawn into two wires $1\, mm$ and $2\, mm$ thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio

A bulb has specification of one kilowatt and $250\, volts$, the resistance of bulb is .................. $\Omega$

An electric kettle has two heating coils. When one coil is used, water in the kettle boils in $5$ minutes, while when second coil is used, same water boils in $10\,\min$. If the two coils, connected in parallel are used simultaneously, the same water will boil in time

Two bulbs of equal wattage, one having carbon filament and the other having a tungsten filament are connected in series to the mains, then

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