Electric Current Concepts - Class 10

Electric Current

• Electric current (I) is defined as the rate of flow of charge through a cross-section of a wire.
• Formula: ( I = \frac{q}{t} ), where ( q ) is charge and ( t ) is time.
• SI unit: ampere (A); conventional direction aligns with positive charge movement.
• Current remains constant across different cross-sections of a conductor; smaller cross-sections mean higher charge flow speed, larger cross-sections mean slower speed.
• For a charge ( q ) revolving in a circle, the equivalent current is ( i = qf ), where ( f ) is frequency.
• In metallic conductors, current is due to free electron motion; in electrolytes and ionized gases, both electrons and positive ions contribute to current.

Types of Electric Current

• Direct Current (DC):

  • Constant magnitude and direction over time.
  • Common sources include batteries and DC dynamos.

• Alternating Current (AC):

  • Magnitude varies continuously and direction changes periodically.
  • Source typically includes AC dynamos.

Current Density

• Current density (J) refers to electric current flowing per unit area of a conductor's cross-section.
• Formula: ( J = \frac{I}{A} ) with SI unit: ampere per square meter (A/m²).
• Current density is a vector quantity, directed along the motion of positive charge.

Thermal and Drift Velocity of Electrons

• Thermal Velocity:

  • Free electrons in metals randomize their movement at high speeds, approximately ( 10^5 ) m/s.
  • Average thermal velocity is zero in any specific direction.

• Drift Velocity:

  • Under an electric field, free electrons move with an average velocity opposite to the field direction, termed drift velocity.
  • Formula for drift velocity: ( v_d = \frac{eEτ}{m} ) or ( v_d = \frac{eVτ}{ml} ).
  • ( τ ): relaxation time, ( e ): charge on an electron, ( E ): electric field intensity, ( l ): conductor length, ( V ): potential difference, ( m ): electron mass.

• Drift velocity relates to current by ( v_d = \frac{I}{nAe} ).

Mobility

• Mobility of electrons (μ) is drift velocity per unit electric field.
• Formula: ( μ = \frac{v_d}{E} ).
• SI unit: m²/(s·V), dimensional formula: [M⁻¹T²A].

Ohm’s Law

• Ohm’s Law states that current (I) is directly proportional to the potential difference (V) under constant physical conditions, particularly temperature.
• Relation: ( I ∝ V ) or ( V = IR ), where R is the electrical resistance.
• Resistance formula: ( R = \frac{ρl}{A} ).

Electrical Resistance

• Defined as the obstruction to current flow within a conductor.
• Formula: ( R = \frac{V}{I} ).
• SI unit: ohm (Ω) with dimensional formula: [ML²T⁻³A⁻²].

Resistivity

• Resistivity (ρ) of a conductor material: ( ρ = \frac{m}{n²τ} ) where ( n ) is the number of free electrons per unit volume.
• Resistance depends on temperature and material properties but is independent of conductor shape or size.