Two wires have resistances of $2 \ \Omega$ and $4 \ \Omega$ and are connected to the same voltage. The ratio of heat dissipated in the resistances is:

The battery of a mobile phone is rated as $4.2 \ V, 5800 \ mAh$. How much energy is stored in it when fully charged (in $kJ$)?

An electric bulb marked as $50 W - 200 V$ is connected across a $100 V$ supply. The present power of the bulb is (in $W$)

An electric fan and a heater are marked as $100 \ W, 220 \ V$ and $1000 \ W, 220 \ V$ respectively. The resistance of the heater is

$A$ constant potential difference is applied to the ends of a graphite rod, whose resistance decreases with a rise in temperature. The rod can be $(1)$ covered with asbestos or $(2)$ left open to the atmosphere. Answer for the steady state.

$A$ 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 $\pi$)?