Current Electricity - Detailed Notes

Topics to Be Covered

  • Electric Current, Ohm's Law, Current Density

  • Electrical Circuits, Wheatstone Bridge

  • Kirchhoff's Laws, Cells, EMF, Power

  • Electrical Instruments, RC Circuits

Electric Current

  • Definition: The rate of flow of electric charge per unit time through a given area.

  • Direction: Along the flow of positive charge; opposite to the flow of negative charge.

  • SI unit: Coulomb (C) or Ampere (A) - one of the seven fundamental quantities in SI.

  • Current is a scalar quantity; it has direction and magnitude but does not follow the rules of vector addition.

Current Density

  • Current density (J) defined as current per unit area [ J = \frac{I}{A} ]

Kirchhoff's Laws

  1. Junction (Current) Law: The algebraic sum of currents entering a junction equals the sum of currents leaving the junction (conservation of charge).

  2. Voltage (Loop) Law: The algebraic sum of potential differences in a closed loop is zero (conservation of energy).

Ohm's Law

  • The current in a conductor is directly proportional to the potential difference (voltage), provided that other conditions (temperature, material) remain constant.

  • Mathematically expressed as [ V = IR ], where R is the resistance.

Resistance and Conductivity

  • Resistance varies with physical factors:

    • Length (l): Longer conductors have higher resistance.

    • Area (A): Wider cross-sections reduce resistance.

    • Resistivity (ρ) is a material specific property that affects resistance.

  • Unit of resistance: Ohm (Ω) [ R = \frac{V}{I} ].

  • Units for conductivity are the inverse of resistance: [ \sigma = \frac{1}{R} ].

Wheatstone Bridge

  • A configuration used to measure unknown resistances by balancing two legs of a bridge circuit.

  • Condition for balance: [ R1 / R2 = R3 / R4 ], where R1, R2 are known resistors, and R_3 is the unknown resistor.

Electrical Circuits

Series Combination

  • Total resistance [ Rs = R1 + R2 + R3 + \cdots ]

  • Current is the same through all components.

Parallel Combination

  • Total resistance [ \frac{1}{Rp} = \frac{1}{R1} + \frac{1}{R_2} + \cdots ]

  • Voltage is the same across all components.

RC Circuits

  • Charging of a capacitor defined by [ q(t) = CV(1 - e^{-t/RC}) ]

  • Discharging characterized by [ q(t) = q_0 e^{-t/RC} ]

Drift Velocity

  • The average drift velocity of charge carriers under an electric field is given by: [ v_d = \frac{I}{nAe} ] where n is the charge carrier density, A is the cross-sectional area, and e is the charge of an electron.

Electrical Instruments

  • Ammeter: Measures current, connected in series.

  • Voltmeter: Measures voltage, connected in parallel.

  • Galvanometer: Detects small currents.

Important Formulas

  • Ohm's Law: [ V = IR ]

  • Power: [ P = IV = I^2R = \frac{V^2}{R} ]

  • Capacitance in RC circuits: [ q = CV ]

  1. Which of the following is the unit of electric current?

    • A) Ohm

    • B) Ampere

    • C) Volt

    • D) Coulomb

  2. According to Ohm's Law, voltage is:

    • A) Inversely proportional to current

    • B) Mass of a charged particle

    • C) Proportional to current

    • D) Independent of resistance

  3. What is the formula for calculating current density?

    • A) J = A/I

    • B) J = I/A

    • C) J = A/V

    • D) J = V/I

  4. In a series circuit, the total resistance is equal to:

    • A) R1 + R2 + R3

    • B) 1/(1/R1 + 1/R2 + 1/R3)

    • C) R1 × R2 × R3

    • D) None of the above

  5. The average drift velocity of charge carriers is given by:

    • A) v_d = I/nAe

    • B) v_d = A/Ine

    • C) v_d = nAe/I

    • D) v_d = I/eA

  6. An ammeter is used to measure:

    • A) Voltage

    • B) Current

    • C) Resistance

    • D) Power

  7. The unit of resistance is:

    • A) Ohm

    • B) Ampere

    • C) Volt

    • D) Joule

  8. What is the function of a galvanometer?

    • A) Measure voltage

    • B) Detect small currents

    • C) Measure resistance

    • D) None of the above