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Current Electricity

NCERT Class 12 Physics Chapter 3

Current Electricity for Class 12 Physics, JEE and NEET: Ohm’s law, drift velocity, resistivity, cells, Kirchhoff’s rules, Wheatstone and metre bridges.

15 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part I (Class 12), Chapter 3 “Current Electricity”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.2 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Electric current

    I = q/t, the net charge q − q, current at an instant as dQ/dt, the ampere and electrons per second.

    NCERT Sections 3.1–3.2 10 min read 4 solved examples 6 practice questions

  2. Electric currents in conductors

    Free electrons in metals, random motion and no net current, and why a cell keeps a steady field.

    NCERT Section 3.3 10 min read 4 solved examples 6 practice questions

  3. Ohm’s law

    V = RI, how R depends on length and area, R = ρl/A, current density, conductivity and j = σE, with examples.

    NCERT Section 3.4 10 min read 4 solved examples 7 practice questions

  4. Experiment: resistance of a wire using Ohm’s law

    a wire’s resistance from the ammeter–voltmeter circuit and rheostat, the V–I graph slope, errors and precautions.

    JEE and NEET only 11 min read 5 solved examples 6 practice questions

  5. Drift of electrons and the origin of resistivity

    Relaxation time, vd = −eEτ/m, the relation I = neAvd, conductivity σ = neτ/m and mobility μ = eτ/m.

    NCERT Section 3.5 12 min read 4 solved examples 7 practice questions

  6. Limitations of Ohm’s law

    Non-ohmic conductors, V–I graphs that bend, the diode’s one-way current and GaAs, with examples.

    NCERT Section 3.6 9 min read 4 solved examples 6 practice questions

  7. Resistivity of various materials

    Conductors, semiconductors and insulators, the range for metals, and the role of impurities.

    NCERT Section 3.7 7 min read 4 solved examples 6 practice questions

  8. Temperature dependence of resistivity

    ρ = ρ[1 + α(T − T)], metals, nichrome, semiconductors, with examples.

    NCERT Section 3.8 10 min read 4 solved examples 6 practice questions

  9. Electrical energy and power

    P = IV = IR = V/R derived, why resistors heat up, kWh, and why power lines use high voltage.

    NCERT Section 3.9 10 min read 4 solved examples 6 practice questions

  10. Combination of resistors: series and parallel

    The combination formulas R = R + R and 1/R = 1/R + 1/R derived, dividers and reducing networks.

    JEE and NEET only 11 min read 4 solved examples 6 practice questions

  11. Cells, emf and internal resistance

    Emf vs terminal voltage, V = ε − Ir, I = ε/(R + r), charging, NCERT exercises.

    NCERT Section 3.10 11 min read 4 solved examples 6 practice questions

  12. Cells in series and in parallel

    The equivalent emf and internal resistance, reversed cells, identical cells and mixed grouping.

    NCERT Section 3.11 11 min read 4 solved examples 6 practice questions

  13. Kirchhoff’s rules

    Junction and loop rules, why they hold, sign conventions, and NCERT Examples 3.5, 3.6 and Exercise 3.7 solved.

    NCERT Section 3.12 13 min read 4 solved examples 6 practice questions

  14. Wheatstone bridge

    Its principle, the balance condition R/R = R/R derived, an unknown resistance, and NCERT Example 3.7.

    NCERT Section 3.13 11 min read 4 solved examples 6 practice questions

  15. Metre bridge and the resistivity of a wire

    S = R(100 − l)/l, balance length, end corrections, precautions, and a wire’s resistivity from its length and diameter.

    JEE and NEET only 12 min read 4 solved examples 9 practice questions

Key formulas in this chapter

Electric current

  • I = q/t (steady current)
  • q = q − q
  • I(t) = lim ΔQ/Δt = dQ/dt
  • 1 A = 1 C s
  • electrons per second: n = I/e

Electric currents in conductors

  • no field: random motion, net current zero
  • metallic solid conductor: electrons move, positive ions fixed
  • electrolyte: both positive and negative ions move
  • fixed end charges: brief current only
  • steady field (cell, battery): steady current

Ohm’s law

  • V = RI
  • R = ρl/A
  • j = I/A
  • E = ρj
  • j = σE, with σ = 1/ρ

Experiment: resistance using Ohm’s law

  • V = RI
  • R = slope of the V–I graph = ΔV/ΔI
  • resistance per unit length = R/l
  • ρ = RA/l, with A = πr
  • I–V graph: slope = 1/R

Drift of electrons

  • vd = −eEτ/m
  • I = neA|vd|
  • σ = neτ/m, ρ = m/(neτ)
  • μ = |vd|/E = eτ/m
  • σ = neμ

Limitations of Ohm’s law

  • ohmic: V–I graph a straight line through the origin
  • (a) V not proportional to I
  • (b) I depends on the sign of V (diode)
  • (c) more than one V for one I (GaAs)
  • non-ohmic: V/I changes from point to point

Resistivity of various materials

  • metals: ρ ≈ 10 to 10 Ω m
  • insulators: ρ ≥ 10 × metals
  • semiconductors: in between
  • semiconductors: ρ falls as T rises
  • cube of side L: R = ρ/L

Temperature dependence of resistivity

  • ρ(T) = ρ[1 + α(T − T)]
  • α = [ρ(T) − ρ]/[ρ(T − T)]
  • R = R[1 + α(T − T)]
  • ρ = m/(neτ)
  • metals: α > 0; semiconductors: ρ falls as T rises

Electrical energy and power

  • P = IV
  • P = IR = V/R
  • ΔW = IVΔt
  • Pc = I2 Rc = P2 Rc/V2
  • 1 kWh = 3.6 × 10 J

Combination of resistors

  • series: Rs = R1 + R2 + R3 + …
  • parallel: 1/Rp = 1/R1 + 1/R2 + 1/R3 + …
  • two in parallel: Rp = R1 R2/(R1 + R2)
  • series divider: V1 = V R1/(R1 + R2)
  • parallel divider: I1 = I R2/(R1 + R2)

Cells, emf and internal resistance

  • ε = V + V (open circuit)
  • V = ε − Ir (discharging)
  • I = ε/(R + r)
  • largest current ε/r
  • V = ε + Ir (charging)

Cells in series and in parallel

  • series: εeq = ε1 + ε2, req = r1 + r2
  • reversed cell: εeq = ε1 − ε2
  • parallel: 1/req = 1/r1 + 1/r2
  • parallel: εeq/req = ε1/r1 + ε2/r2
  • n identical: series nε, nr; parallel ε, r/n

Kirchhoff’s rules

  • junction: sum of currents in = sum of currents out
  • loop: sum of potential changes = 0
  • along I through R: −IR; against: +IR
  • cell − to +: +ε; + to −: −ε
  • cube of equal R, opposite corners: Req = 5R/6

Wheatstone bridge

  • balance: R2/R1 = R4/R3
  • unknown: R4 = R3 R2/R1
  • opposite arms: R1 R4 = R2 R3
  • at balance: Ig = 0, I1 = I3, I2 = I4
  • balanced bridge: middle arm carries no current
  • NCERT Example 3.7: Ig ≈ 4.87 mA

Metre bridge

  • balance: R/S = l/(100 − l)
  • S = R(100 − l)/l
  • ρ = πdS/(4L)
  • error: Δρ/ρ = ΔS/S + 2Δd/d + ΔL/L
  • best balance point: near the middle of the wire

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