What is electric power? Derive its different formulae.

Electric Power is the rate at which electrical energy is converted into other forms of energy, such as heat, light, or mechanical energy, in an electrical circuit. The unit of electric power is the watt (W), and it is often used to express the rate at which energy is consumed or produced in electrical devices, such as motors, light bulbs, and appliances.

Formulae for Electric Power

  1. Basic Formula: Electric power PP is given by the product of voltage () and current ():

    P=V×I

    Where:

    • = electric power (in watts, W)
    • = voltage (in volts, V)
    • = current (in amperes, A)

  2. Using Ohm’s Law: Ohm’s law states that V=I×R, where is the resistance of the circuit. By substituting this into the basic power formula, we can derive two other forms:

    • Power in terms of current and resistance:

      P=I2×R

      This formula expresses power in terms of the current and the resistance in the circuit.

    • Power in terms of voltage and resistance: By substituting I=V/R from Ohm’s law into the basic formula, we get:

      P=V2/R

      This expresses power in terms of the voltage and resistance.

Summary of Electric Power Formulae:

  1. P=V×I
  2. P=I2×R
  3. P=V2/R

Explanation of Each Formula:

  • P=V×I: This is the most general formula for electric power, representing the rate at which energy is transferred when a voltage causes a current to flow through a circuit.

  • P=I2×R: This formula is derived by combining the basic power equation with Ohm’s law. It is particularly useful when you know the current and the resistance but not the voltage.

  • P=V2/R This formula is useful when you know the voltage and the resistance in a circuit but not the current.

These three formulas are essential for solving problems related to power consumption in electrical circuits.

Related Questions:

  1. If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?
  2. Two electric bulbs marked 100 W, 220 V and 200 W, 220 V have tungsten filaments of the same length. Which bulb has a thicker filament?
  3. Show that Volt-Ampere is equal to Watt (SI unit of power).
  4. Define and explain the term electric current. What is the difference between electronic current and conventional current?
  5. How can you differentiate between emf and potential difference? What do you mean by emf? Is it really a force? Explain
  6. Explain Ohm’s Law. What are its limitations? Differentiate between ohmic and non-ohmic conductors.
  7. Analyze IV characteristic graphs for a metallic conductor, an incandescent bulb, and a thermistor to determine ohmic and non-ohmic behavior.
  8. Define resistance and its unit. What is the cause of resistance? On what factors does the resistance of a metallic conductor depend?
  9. How are resistances connected in series? What are their characteristics? Derive the formula for equivalent resistance.
  10. How are resistances connected in parallel? What are their characteristics? Derive the formula for equivalent resistance.
  11. In a circuit, three bulbs are connected in series and in another circuit, three bulbs are connected in parallel. The magnitude of the emf source for both circuits is the same. How can you explain the difference in brightness of bulbs in both circuits?
  12. State and prove Joule’s law of heating.
  13. Define kilowatt-hour (kWh). What is its relation with joule? How can you calculate energy in kWh by a formula?
  14. 12. Differentiate between direct current (DC) and alternating current (AC). Define the following terms for AC: (i) Cycle, (ii) Time period, (iii) Frequency.
  15. What is the function of a galvanometer, ammeter, and voltmeter? How are they connected in circuits?
  16. How is electricity supplied to houses by the electricity department? How do we distribute it in household circuits?
  17. What do you mean by short circuit and open circuit? Define live wire, neutral wire, and earth wire in household circuits.
  18. Describe the hazards of household electricity and four safety measures.
  19. Can current flow through a circuit without potential difference? Explain.
  20. Can current flow through a circuit without potential difference? Explain.