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. The ratio of heat produced in the wires is:

Two heating coils of resistances $10 \Omega$ and $20 \Omega$ are connected in parallel and connected to a battery of emf $12 \text{ V}$ and internal resistance $1 \Omega$. The ratio of the power consumed by them is:

Two electric bulbs $A$ and $B$ are rated as $60\, W$ and $100\, W$. They are connected in parallel to the same source. Then,

An electric power line having a total resistance of $2 \ \Omega$ delivers $1 \ kW$ of power at $250 \ V$. The percentage efficiency of the transmission line is: (in $\%$)

$A$ circular wire has a current density $J = (2 \times 10^{10} \text{ A/m}^2) r^2$, where $r$ is the radial distance from the center and the wire radius is $2 \text{ mm}$. The potential difference applied across the wire is $50 \text{ V}$. How much energy (in Joules) is converted to thermal energy in $100 \text{ s}$ (in $\pi$)?

$A$ given quantity of water is boiled by an electric heater in $5 \text{ min}$. If the supply voltage of the heater is reduced to half,then the time taken to boil the same quantity of water will be . . . . . . $\text{min}$. (Assume the resistance of the heater remains constant.)