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Current Electricity – Complete Formula, Laws & PYQ Profiling

Current Electricity – Complete Formula, Laws & PYQ Profiling (JEE Main Only)

1. Electric Current & Drift Velocity

  • Electric current: I = Q / t
  • Current density: J = nqvd
  • Drift velocity: vd = eEτ / m
  • Relation: I = nAevd
  • Mobility: μ = vd / E
  • Conductivity: σ = nqμ
  • Resistivity: ρ = 1 / σ

JEE Trap: Drift velocity is extremely small, but electrical signal propagates almost at speed of light.

2. Ohm’s Law & Resistance

  • Ohm’s law: V = IR
  • Resistance: R = ρL / A
  • Temperature dependence: R = R₀(1 + αΔT)

Combination of resistors:

  • Series: Req = R₁ + R₂ + …
  • Parallel: 1/Req = 1/R₁ + 1/R₂ + …

PYQ Trap: For same material & volume, R ∝ L² (since A ∝ 1/L).

3. Electric Power & Heating Effect

  • P = VI = I²R = V² / R
  • Electrical energy: E = Pt
  • Joule’s law of heating: H = I²Rt

4. EMF & Internal Resistance

  • Terminal voltage (discharging): V = E − Ir
  • Terminal voltage (charging): V = E + Ir
  • Current: I = E / (R + r)
  • Maximum power transfer: R = r
  • Efficiency: η = R / (R + r)

High-frequency JEE point: Maximum power ≠ maximum efficiency.

5. Kirchhoff’s Laws (Core JEE Area)

(a) Kirchhoff’s Current Law (KCL):

ΣIin = ΣIout

At any junction, algebraic sum of currents is zero (charge conservation).

(b) Kirchhoff’s Voltage Law (KVL):

ΣΔV = 0

  • In any closed loop, sum of potential differences is zero
  • Based on conservation of energy

Sign conventions (very important):

  • Across resistor along current → −IR
  • Across resistor opposite to current → +IR
  • Battery (− to +) → +E
  • Battery (+ to −) → −E

Common Mistakes: Wrong polarity of cell, ignoring internal resistance, mixing loop currents.

6. Wheatstone Bridge & Meter Bridge

  • Balanced condition: P / Q = R / S
  • Meter bridge: X / R = l / (100 − l)
  • At balance point, galvanometer current = 0

7. Galvanometer, Ammeter & Voltmeter

  • Ammeter shunt: S = (G Ig) / (I − Ig)
  • Voltmeter resistance: R = (V / Ig) − G
  • Ammeter → low resistance
  • Voltmeter → high resistance

PYQ Focus: Conversion formulas directly asked in JEE Main.

8. JEE Main Question Profiling

Topic Question Nature Frequency
KCL + KVL 2-loop numerical High
EMF & r Direct formula High
Drift velocity Conceptual MCQ Medium
Meter bridge Balance length Medium
Power & heating Direct numeric High

StudyBeacon • JEE Main Physics • Current Electricity (Final Integrated Version)

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