# Electric Power **Electric power** is the rate at which electrical energy is transferred by an electric circuit. It is the amount of energy consumed or produced per unit time. Understanding electric power is essential for analyzing circuits and managing energy consumption. ## Categories of Electric Power **DC Power (Direct Current):** In a DC circuit, the electric charge flows in only one direction. This type of power is supplied by batteries. **AC Power (Alternating Current):** In an AC circuit, the electric charge periodically reverses direction. This type of power is delivered to homes and businesses from the power grid. AC is preferred for long-distance transmission because its voltage can be easily stepped up or down with transformers. ## Electric Power Formulas Electric power ($P$) can be calculated using several equivalent formulas, depending on the known quantities in a circuit. The fundamental definition is the rate of energy transfer: $$ P = \frac{\text{Energy}}{\text{Time}} = \frac{E}{t} $$ Since the energy transferred to a charge $Q$ by a potential difference $V$ is $E = VQ$, we have: $$ P = \frac{VQ}{t} $$ Given that current $I = Q/t$ (the rate of charge flow), the most common power formula is: $$ P = VI $$ Using Ohm's Law ($V=IR$), we can derive two other useful forms: 1. In terms of current and resistance: $$ P = (IR)I = I^2R $$ 2. In terms of voltage and resistance: $$ P = V\left(\frac{V}{R}\right) = \frac{V^2}{R} $$ ## Energy Dissipation in a Resistor When current flows through a resistor, electrical energy is converted into heat. This is known as **power dissipation** or **Joule heating**. The electrical energy dissipated as heat over a time period $t$ is: $$ \text{Energy Dissipated} (E) = P \times t = VIt = I^2Rt = \frac{V^2}{R}t $$ ## Units of Electric Power and Energy **SI Unit of Power:** The **Watt (W)**. It is a . $$ 1 \, \text{Watt} = 1 \, \text{Joule/second} = 1 \, \text{Volt} \times 1 \, \text{Ampere} $$ **Commercial Unit of Energy:** Electrical energy is commercially sold in units of **Kilowatt-hours (kWh)**. One kWh is the energy consumed by a 1-kilowatt (1000 W) device operating for one hour. $$ 1 \, \text{kWh} = (1000 \, \text{W}) \times (3600 \, \text{s}) = 3.6 \times 10^6 \, \text{Joules} $$ ## Example Calculation **Problem:** Calculate the monthly cost of using a 50 W light bulb for 8 hours daily, if the price of electricity is Rs. 20 per unit (per kWh). Assume a 30-day month. **Solution:** 1. Calculate total operating time: $$ \text{Time} = 8 \, \text{hours/day} \times 30 \, \text{days} = 240 \, \text{hours} $$ 2. Calculate total energy consumed in kWh (units): $$ \text{Energy (kWh)} = \frac{\text{Power (W)} \times \text{Time (h)}}{1000} $$ $$ \text{Energy} = \frac{50 \, \text{W} \times 240 \, \text{h}}{1000} = 12 \, \text{kWh} $$ 3. Calculate the total cost: $$ \text{Cost} = \text{Energy (kWh)} \times \text{Cost per unit} $$ $$ \text{Cost} = 12 \times 20 = \text{Rs. } 240 $$ | Concept | Formula(s) | SI Unit | | :--- | :--- | :--- | | **Power** | $P = VI = I^2R = V^2/R$ | Watt (W) | | **Energy** | $E = P \times t$ | Joule (J) or kWh |