11.11 Electric Power

Electric power is the rate at which electrical energy is transferred by an electric circuit — the amount of energy consumed or produced per unit time.

Electric Power Formulas

The fundamental definition of electric power is: $P=\frac{\text{Energy}}{\text{Time}}=\frac{E}{t}$

Since the energy transferred to a charge $Q$ by a potential difference $V$ is $E=VQ$, and current $I=Q/t$: $P=\frac{VQ}{t}=VI$

Using Ohm's Law ($V=IR$), two further equivalent forms are derived:

1. In terms of current and resistance: $P=I^{2}R$

2. In terms of voltage and resistance: $P=\frac{V^2}{R}$

Energy Dissipation in a Resistor (Joule Heating)

When current flows through a resistor, electrical energy is converted into heat. This is called Joule heating or power dissipation. The electrical energy dissipated over time $t$ is: $E=P\times t=VIt=I^{2}Rt=\frac{V^2}{R}t$

Units of Electric Power and Energy

SI Unit of Power: The Watt (W). It is a Derived Unit→. $1\text{W}=1\text{J/s}=1\text{V}\times 1\text{A}$

Commercial Unit of Energy: Electrical energy is commercially sold in Kilowatt-hours (kWh). One kWh is the energy consumed by a 1 kW device operating for one hour. $1\text{kWh}=1000\text{W}\times 3600\text{s}=3.6\times 10^6\text{J}$

Summary Table

Worked Example

Problem: Calculate the monthly cost of using a 50 W light bulb for 8 hours daily, if electricity costs Rs. 20 per kWh. Assume a 30-day month.

Solution:

1. Total operating time: $\text{Time}=8\text{h/day}\times 30\text{days}=240\text{h}$

2. Total energy consumed: $\text{Energy}=\frac{50\text{W}\times 240\text{h}}{1000}=12\text{kWh}$

3. Total cost: $\text{Cost}=12\times 20=\text{Rs. }240$