State and prove Joule’s law of heating.

Joule’s Law of Heating

Joule’s Law of Heating states that the amount of heat produced by a current passing through a conductor is directly proportional to:

  1. The square of the current (I2),
  2. The resistance of the conductor (),
  3. The time () for which the current flows.

Mathematically, Joule’s Law is expressed as:

Q=I2Rt

Where:

  • Q is the heat produced (in joules),
  • I is the current flowing through the conductor (in amperes),
  • is the resistance of the conductor (in ohms),
  • is the time the current flows (in seconds).

Proof of Joule’s Law

To derive Joule’s Law, we start with the definition of electrical power.

  1. Power Dissipated: The power dissipated in a resistor due to the current flowing through it is given by:

P=VI

Where:

  • V is the potential difference (voltage) across the resistor,
  • is the current.
  1. Ohm’s Law: According to Ohm’s Law, the relationship between voltage , current I, and resistance is:

V=IR

  1. Substitute in the power formula: We can substitute V=IR into the power equation:

P=I×IR=I2R

This shows that the power dissipated is proportional to the square of the current and the resistance of the conductor.

  1. Heat Produced: The total heat produced over a time interval is the energy dissipated, which is the power multiplied by time:

Q=P×t

Substitute P=I2R into the equation:

Q=I2R×t

Thus, we obtain the expression for heat dissipated:

Q=I2Rt

This is Joule’s Law of Heating, showing that the heat produced is directly proportional to the square of the current, the resistance of the conductor, and the time for which the current flows.

Implications of Joule’s Law:

  • Current: Higher current leads to greater heat dissipation.
  • Resistance: A higher resistance in the conductor will also lead to more heat production.
  • Time: The longer the current flows, the more heat is generated.

Example:

If a current of 2 A flows through a resistor of resistance 5 Ω for 10 seconds, the heat produced is:

Q=I2Rt=(2)2×5×10=4×5×10=200 Joules

Thus, 200 joules of heat will be produced.

In conclusion, Joule’s Law is a fundamental principle that explains how electrical energy is converted into heat energy when current flows through a resistor

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. What is electric power? Derive its different formulae.
  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.