Q.A toaster operating at 240 V has a resistance of 120 $\Omega$. Its power is

Deriving P = VI. Tracking a small positive charge dQ around a simple loop containing a battery of voltage V and a resistor: moving through the battery, the charge gains potential energy $dU=V\,dQ$ (at the expense of the battery's stored chemical energy); moving through the resistor, it loses that same energy to collisions with the resistor's atoms. The rate at which this energy is delivered is the electrical power, $P=dU/dt=V\,dQ/dt$, and since $I=dQ/dt$,

This gives the power delivered by a battery (or delivered TO any electrical device) carrying current I under potential difference V, with SI unit the watt ($1\ \text{W}=1\ \text{J/s}$).

Alternative forms via Ohm's law. Substituting $V=IR$ into $P=VI$ gives $P=I^2R$, and substituting $I=V/R$ instead gives $P=V^2/R$ -- three algebraically equivalent expressions for the power dissipated in a resistor, each convenient in different situations depending on which quantity (I or V) is already known. The $I^2R$ (and $V^2/R$) forms make clear that power depends on the SQUARE of current (or voltage): doubling the current through a fixed resistor quadruples, not merely doubles, the power dissipated.

Comparing bulbs in series versus parallel. Because $P=V^2/R$ shows that resistance is inversely proportional to power for a FIXED voltage rating, a lower-wattage bulb actually has a HIGHER resistance than a higher-wattage bulb of the same voltage rating. This has a genuinely counter-intuitive consequence: connected in PARALLEL (same voltage, $P\propto I$), the higher-wattage bulb draws more current and glows brighter, exactly as one would naively expect; but connected in SERIES (same current, $P=I^2R$), it is instead the bulb with the HIGHER resistance -- i.e. the lower rated wattage -- that dissipates more power and glows brighter, exactly the opposite of the parallel case. This same resistance mismatch is also why, when two differently-rated bulbs are connected in series to a supply exceeding either bulb's rated voltage, it is typically the LOWER-wattage (higher-resistance) bulb that ends up absorbing most of the excess voltage and blows first.

Energy and billing. Electrical energy is simply power sustained over time (power multiplied by duration); because a joule is far too small a unit for household billing, energy is commercially measured in kilowatt-hours (kWh), where $1\ \text{kWh}=(1000\ \text{W})(3600\ \text{s})=3.6\times10^6$ J (also called "1 unit" of electricity). Electricity boards bill customers for total ENERGY consumed, not power -- so a high-power appliance run briefly and a low-power appliance run for a correspondingly longer time can cost exactly the same.