Electric Current And Current Density – An introduction

• Electric current is the flow of electric charge.
• It is the rate of flow of charge through a cross-sectional area.
• The SI unit of electric current is the ampere (A).
• Symbol for electric current is I.
• Current can be direct (DC) or alternating (AC).

Definition of Electric Current

• Electric current is defined as the rate of flow of electric charge through a conductor.
• It is given by the equation: I = ΔQ/Δt
  • I: electric current
  • ΔQ: change in charge
  • Δt: time taken

Symbol Convention for Current

• The direction of conventional current (Ic) is considered as the direction of flow of positive charges.
• In reality, the flow of electrons is opposite to the direction of conventional current.
• Symbol for conventional current is Ic.

Electric Current and Drift Velocity

• In a metallic conductor, current is carried by the free electrons.
• These electrons keep colliding with atoms and move randomly called thermal motions.
• The net flow of electrons constitutes the electric current.
• Average velocity of electrons constitutes the drift velocity.

Relation between Current and Drift Velocity

• The electric current (I) flowing through a conductor can be related to the drift velocity (v) of the charge carriers using the equation:
  • I = nAvQ
    • I: electric current
    • n: number density of charge carriers
    • A: cross-sectional area of the conductor
    • v: drift velocity
    • Q: charge of each charge carrier

Current Density

• Current density (J) is defined as the current per unit cross-sectional area.
• It is given by the equation: J = I/A
  • J: current density
  • I: electric current
  • A: cross-sectional area

Relation between Current Density and Drift Velocity

• The current density (J) can also be related to the drift velocity (v) using the equation:
  • J = nev
    • J: current density
    • n: number density of charge carriers
    • e: charge of each charge carrier
    • v: drift velocity

Direction of Current Density

• The direction of current density (J) is always perpendicular to the cross-sectional area (A).
• It is in the direction of flow of positive charge carriers in a conductor.

Resistance and Resistivity

• Resistance (R) is the property of a conductor to oppose the flow of electric current.
• It is given by the equation: R = V/I
  • R: resistance
  • V: potential difference applied
  • I: electric current flowing through the conductor

11. Ohm’s Law

• Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference applied across it, provided the temperature remains constant.
• Mathematically, Ohm’s Law can be expressed as: V = IR
  • V: potential difference
  • I: electric current
  • R: resistance

12. Conductors and Insulators

• Conductors are materials that allow the flow of electric current through them easily due to the presence of free electrons.
• Examples of conductors include metals like copper, aluminum, etc.
• Insulators are materials that do not allow the flow of electric current through them due to the absence of free electrons.
• Examples of insulators include rubber, plastic, glass, etc.

13. Resistivity of Materials

• Resistivity (ρ) is a property of a material that determines its resistance.
• Resistivity is given by the equation: ρ = R(A/L)
  • ρ: resistivity
  • R: resistance
  • A: cross-sectional area of the conductor
  • L: length of the conductor

14. Factors Affecting Resistance

• Resistance depends on the resistivity of the material, length of the conductor, and its cross-sectional area.
• Resistance is directly proportional to the length of the conductor and its resistivity.
• Resistance is inversely proportional to the cross-sectional area of the conductor.
• A thicker and shorter conductor has less resistance compared to a thinner and longer conductor.

15. Ohmic and Non-Ohmic Conductors

• Ohmic conductors follow Ohm’s Law, i.e., their resistance remains constant with varying potential difference.
• Non-Ohmic conductors do not follow Ohm’s Law, i.e., their resistance changes with varying potential difference.
• Examples of Ohmic conductors include most metals.
• Examples of Non-Ohmic conductors include diodes, transistors, etc.

16. Current-Voltage Characteristics

• Current-voltage characteristics represent the relationship between current and voltage for a given circuit or component.
• The shape of the current-voltage curve can vary depending on the nature of the circuit or component.
• Ohmic conductors have a linear current-voltage characteristic, while non-Ohmic conductors have nonlinear characteristics.

17. Power in Electric Circuits

• Power (P) in an electric circuit is the rate at which electric energy is transferred or consumed.
• Power is given by the equation: P = IV
  • P: power
  • I: electric current
  • V: potential difference

18. Energy Transformation in Electric Circuits

• In an electric circuit, electrical energy is transformed into heat energy due to the resistance in the circuit.
• The power dissipated as heat in a resistor is given by the equation: P = I^2R = V^2/R

19. Kirchhoff’s Laws

• Kirchhoff’s laws are fundamental principles used for analyzing and solving complex electrical circuits.
• Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering and leaving a junction in a circuit is zero.
• Kirchhoff’s voltage law (KVL) states that the algebraic sum of potential differences in any closed loop of a circuit is zero.

20. Series and Parallel Circuits

• In a series circuit, components are connected one after the other. The same current (I) flows through each component, and the total resistance (R) is the sum of individual resistances.

• In a parallel circuit, components are connected across the same potential difference (V). The potential difference across each component is the same, and the total resistance (R) is given by the reciprocal of the sum of reciprocals of individual resistances.

• Electromotive Force (emf)

  • Electromotive Force (emf) is the driving force that pushes the charge around a circuit.
  • It is not a force in the conventional sense, but rather a measure of the energy provided by the source of electric potential difference (battery, generator, etc.)
  • Emf is given by the equation: emf = V + Ir
    • emf: electromotive force
    • V: potential difference across the source
    • I: electric current flowing through the circuit
    • r: internal resistance of the source

• Internal Resistance

  • Internal resistance (r) is the inherent resistance present within the source of emf.
  • It is caused by the resistance of the materials and components within the source, such as the electrolyte in a battery.
  • Internal resistance reduces the emf provided by the source as the electric current increases.
  • Internal resistance can be modeled as a resistor in series with the source of emf.

• Power Dissipated in a Resistor

  • The power dissipated in a resistor (P) is the rate at which energy is transferred or consumed by the resistor in the form of heat.
  • Power is given by the equation: P = IV = I^2R = V^2/R
    • P: power
    • I: electric current flowing through the resistor
    • V: potential difference across the resistor
    • R: resistance of the resistor

• Energy Conservation in Circuits

  • In a closed electric circuit, the total electric potential energy supplied by the source of emf is conserved.
  • This energy is transformed into other forms, such as kinetic energy, heat energy, or light energy, as the electric current flows through the circuit.
  • The total power supplied by the source of emf is equal to the total power dissipated in the resistors and other components in the circuit.

• Resistors in Series

  • In a series circuit, resistors are connected one after the other.
  • The total resistance (Rt) of resistors in series is the sum of individual resistances.
  • The current passing through each resistor in series is the same, and the potential difference across each resistor depends on its individual resistance.

• Resistors in Parallel

  • In a parallel circuit, resistors are connected across the same potential difference.
  • The reciprocal of the total resistance (1/Rt) of resistors in parallel is the sum of reciprocals of individual resistances.
  • The potential difference across each resistor in parallel is the same, and the current passing through each resistor depends on its individual resistance.

• Kirchhoff’s Rules in Circuit Analysis

  • Kirchhoff’s rules, i.e., Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL), are used to analyze complex electrical circuits.
  • Kirchhoff’s current law states that the algebraic sum of currents entering and leaving a junction in a circuit is zero.
  • Kirchhoff’s voltage law states that the algebraic sum of potential differences in any closed loop of a circuit is zero.

• Capacitors and Capacitance

  • Capacitors are passive electronic components that store electrical energy in the form of an electric field.
  • Capacitance (C) is a measure of the ability of a capacitor to store charge.
  • Capacitance is given by the equation: C = Q/V
    • C: capacitance
    • Q: charge stored on the capacitor
    • V: potential difference across the capacitor

• Capacitors in Series and Parallel

  • Capacitors in series have a total capacitance (Ct) given by the reciprocal of the sum of reciprocals of individual capacitances.
  • Capacitors in parallel have a total capacitance (Ct) equal to the sum of individual capacitances.
  • In series, the same charge is stored on each capacitor, while in parallel, the potential difference across each capacitor is the same.