Quick Revision Notes & Formula Sheet

Class 10 Science - Chapter: Electricity (विद्युत)

### Concept 1: Electric Charge & Current (विद्युत आवेश तथा धारा)

• Electric Charge ($Q$): It is the fundamental property of matter. Measured in Coulombs (C).

  • Formula: Q = I × t
  • Charge on an electron ($e$): 1.6 × 10^-19 C
  • Number of electrons ($n$) in a charge $Q$: n = Q / e

• Electric Current ($I$): The rate of flow of electric charge. Measured in Amperes (A).

  • Formula: I = Q / t
  • Direction of current: Opposite to the flow of electrons (conventional current).

### Concept 2: Electric Potential & Potential Difference (विभवांतर)

• Potential Difference ($V$): The work done ($W$) in moving a unit positive charge ($Q$) between two points. Measured in Volts (V).
  • Formula: V = W / Q
  • 1 Volt: When 1 Joule of work is done in moving 1 Coulomb of charge, the potential difference is 1 Volt (1 V = 1 J/C).

### Concept 3: Ohm’s Law (ओम का नियम)

• Statement: At a constant temperature, the current ($I$) flowing through a conductor is directly proportional to the potential difference ($V$) across its ends.
  • Formula: V ∝ I or V = I × R
  • Where $R$ is Resistance (प्रतिरोध), measured in Ohms ($\Omega$).

### Concept 4: Resistance & Factors Affecting It (प्रतिरोध और इसे प्रभावित करने वाले कारक)

• Resistance ($R$): The opposition to the flow of electric current.

• Factors:

  1. Directly proportional to length ($l$): R ∝ l
  2. Inversely proportional to cross-sectional area ($A$): R ∝ 1 / A
  3. Nature of material and temperature.

• Formula: R = ρ × (l / A)

  • Where $\rho$ (Rho) is electrical resistivity (विशिष्ट प्रतिरोध) of the material.
  • SI unit of Resistivity ($\rho$): Ohm-meter ($\Omega \cdot m$).

### Concept 5: Combination of Resistors (प्रतिरोधकों का संयोजन)

• Resistors in Series (श्रेणी क्रम में):

  • Current through each resistor is the same.
  • Equivalent Resistance ($R_s$): R_s = R_1 + R_2 + R_3

• Resistors in Parallel (समांतर क्रम में):

  • Potential difference across each resistor is the same.
  • Equivalent Resistance ($R_p$): 1 / R_p = (1 / R_1) + (1 / R_2) + (1 / R_3)

### Concept 6: Heating Effect of Electric Current (विद्युत धारा का तापीय प्रभाव)

• Electric Work / Energy ($W$ or $H$):

  • H = V × I × t
  • Using Ohm's Law (V = IR), we get:
    • H = I^2 × R × t (Joule's Law of Heating)
    • H = (V^2 / R) × t

• Joule’s Law of Heating: Heat produced in a resistor is:

  1. Directly proportional to the square of current (I^2).
  2. Directly proportional to resistance (R).
  3. Directly proportional to time (t).

### Concept 7: Electric Power (विद्युत शक्ति)

• Electric Power ($P$): The rate at which electric energy is dissipated or consumed. Measured in Watts (W).

  • Formulas:
    • P = V × I
    • P = I^2 × R
    • P = V^2 / R

• Commercial Unit of Electrical Energy:

  • Kilowatt-hour ($kWh$) or Board of Trade (BOT) unit.
  • 1 kWh = 1000 Watts × 3600 seconds = 3.6 × 10^6 Joules (J)
  • 1 Unit = 1 kWh

### Quick Unit Reference Table (महत्वपूर्ण मात्रक)