📝 Chapter Notes & Revision

Current Electricity

🏫 MP BoardClass 12Physics

📐 Formula & Cheat Sheet (English)

Quick Revision Notes

Class 12 Physics - Current Electricity (MP Board)

### 1. Electric Current (विधुत धारा)

  • Definition: The rate of flow of electric charge through any cross-section of a conductor.
  • Formula: I = Q / t
    • Where I = Electric Current (in Ampere, A)
    • Q = Charge (in Coulomb, C)
    • t = Time (in seconds, s)
  • Microscopic View: I = n e A v_d
    • n = Number density of free electrons
    • e = Charge of an electron (1.6 x 10^-19 C)
    • A = Cross-sectional area
    • v_d = Drift velocity

### 2. Drift Velocity and Mobility (अपवाह वेग एवं गतिशीलता)

  • Drift Velocity (v_d): The average velocity with which free electrons get drifted towards the positive terminal under the influence of an applied electric field.
    • Formula: v_d = (e E / m) * tau
    • (e = electronic charge, E = electric field, m = mass of electron, tau = relaxation time)
  • Relation with Current: I = n e A v_d
  • Mobility (mu): Magnitude of drift velocity per unit electric field.
    • Formula: mu = v_d / E
    • SI Unit: m^2 V^-1 s^-1

### 3. Ohm's Law (ओम का नियम)

  • Statement: At constant physical conditions (temperature, pressure, etc.), the current flowing through a conductor is directly proportional to the potential difference across its ends.
  • Formula: V = I R
    • V = Potential Difference (Volt)
    • I = Current (Ampere)
    • R = Electrical Resistance (Ohm, Ω)

### 4. Resistance, Resistivity, and Conductivity (प्रतिरोध, विशिष्ट प्रतिरोध एवं चालकता)

  • Resistance (R): Obstruction to the flow of current.
    • Formula: R = rho * (l / A)
    • rho = Resistivity (Specific Resistance)
    • l = Length of conductor
    • A = Area of cross-section
  • Resistivity (rho): Depends on the material and temperature, not on dimensions.
    • SI Unit: Ω m (Ohm-meter)
  • Conductance (G): Reciprocal of resistance.
    • G = 1 / R (Unit: Ω^-1 or Siemens, S)
  • Conductivity (sigma): Reciprocal of resistivity.
    • sigma = 1 / rho (Unit: Ω^-1 m^-1 or S m^-1)
  • Vector Form of Ohm's Law: J = sigma * E
    • (J = Current density I/A, E = Electric field)

### 5. Temperature Dependence of Resistance (तापमान का प्रतिरोध पर प्रभाव)

  • Resistance of a conductor changes linearly with temperature:
    • R_t = R_0 (1 + alpha * Delta T)
    • R_t = Resistance at t°C
    • R_0 = Resistance at 0°C
    • alpha = Temperature coefficient of resistance
    • Delta T = Change in temperature

### 6. Combination of Resistors (प्रतिरोधों का संयोजन)

  • Series Combination (श्रेणी क्रम):
    • Equivalent Resistance: R_s = R_1 + R_2 + R_3 + ...
    • Current remains the same through each resistor.
  • Parallel Combination (समांतर क्रम):
    • Equivalent Resistance: 1 / R_p = (1 / R_1) + (1 / R_2) + (1 / R_3) + ...
    • Potential difference remains the same across each resistor.

### 7. Electric Cell, EMF, Terminal Voltage, and Internal Resistance (विद्युत सेल, वि.वा.ब., टर्मिनल विभवांतर एवं आंतरिक प्रतिरोध)

  • EMF (E): Potential difference across the terminals of a cell when no current is drawn from it (open circuit).
  • Terminal Voltage (V): Potential difference across the terminals when current is drawn from the cell (closed circuit).
  • Internal Resistance (r): Opposition offered by the electrolyte of the cell.
  • Relation:
    • During discharging: V = E - I r
    • Internal resistance formula: r = ((E - V) / V) * R
    • Current from a cell: I = E / (R + r)

### 8. Combination of Cells (सेलों का संयोजन)

  • Series Grouping:
    • Equivalent EMF = n E
    • Equivalent Internal Resistance = n r
    • Current I = (n E) / (R + n r)
  • Parallel Grouping:
    • Equivalent EMF = E
    • Equivalent Internal Resistance = r / m
    • Current I = (m E) / (m R + r)

### 9. Kirchhoff’s Laws (किरचॉफ के नियम)

  1. Kirchhoff's Current Law (KCL / Junction Rule):
    • The algebraic sum of currents meeting at any junction in a closed circuit is zero.
    • Σ I = 0 (Conservation of Charge)
  2. Kirchhoff's Voltage Law (KVL / Loop Rule):
    • The algebraic sum of changes in potential around any closed loop is zero.
    • Σ (IR) + Σ E = 0 (Conservation of Energy)

### 10. Wheatstone Bridge (व्हीटस्टोन सेतु)

  • An arrangement of four resistances used to determine an unknown resistance.
  • Condition for Balance: No current flows through the galvanometer (I_g = 0).
  • Formula: P / Q = R / S
    • If P, Q, and R are known, unknown resistance S = Q * (R / P)

### 11. Meter Bridge (मीटर सेतु)

  • Based on the principle of Wheatstone Bridge.
  • Formula to find unknown resistance X:
    • X = R * ((100 - l) / l)
    • R = Known resistance in the left gap
    • l = Balancing length from the left end (in cm)
    • (100 - l) = Balancing length from the right end

### 12. Potentiometer (विभवमापी)

  • Used to measure EMF of a cell or compare EMFs of two cells accurately without drawing any current.
  • Potential Gradient (k): Potential drop per unit length of the wire.
    • k = V / L = (I * R) / L
  • Comparison of EMFs of two cells:
    • E_1 / E_2 = l_1 / l_2
    • (l_1, l_2 are balancing lengths for cells E_1 and E_2)
  • Determination of Internal Resistance:
    • r = R * ((l_1 - l_2) / l_2)

### 13. Electric Energy and Power (विद्युत ऊर्जा एवं शक्ति)

  • Electric Work / Energy (W):
    • W = V I t = I^2 R t = (V^2 / R) * t
  • Electric Power (P): Rate at which work is done or energy is consumed.
    • P = V I = I^2 R = V^2 / R
    • SI Unit: Watt (W) or Joule per second.
  • Commercial Unit of Electrical Energy:
    • Kilowatt-hour (kWh) or Board of Trade Unit (BOTU)
    • 1 kWh = 3.6 x 10^6 Joules