Current Electricity Class 12 Physics Formula Sheet 2026-27

Current Electricity Class 12 Physics: Formula Sheet & Quick Revision 2026–27
A compact, exam-focused revision sheet covering the formulas and key results within the current CBSE 2026–27 Chapter 3 syllabus.

CBSE scope: Current Electricity is Chapter 3 under Unit II. The 2026–27 Physics curriculum assigns 17 marks to Unit II Current Electricity at unit level. The curriculum covers current, drift velocity, mobility, current density, Ohm's law and V–I characteristics, power and energy, resistivity and conductivity, temperature dependence, emf/internal resistance, cells, Kirchhoff's rules and Wheatstone bridge.

1. Electric Current & Current Density

I = ΔQ / Δt

Average current = charge flowing through a cross-section per unit time.

I = dQ / dt

Instantaneous current.

J = I / A

Current density magnitude for a uniform current distribution. SI unit: A m⁻².

2. Drift Velocity & Mobility

I = n e A v_d

For electrons, n is number density, e is magnitude of electronic charge, A is cross-sectional area and v_d is drift speed.

v_d = I / (n e A)

μ = v_d / E

Mobility: drift speed per unit electric field.

J = n e v_d

Magnitude relation for current density in a conductor.

3. Ohm's Law & V–I Characteristics

V = IR

For an ohmic conductor under constant physical conditions.

R = V / I

Resistance at the operating point; for an ohmic resistor it remains constant under fixed conditions.

A straight-line V–I characteristic through the origin indicates an ohmic relationship when physical conditions remain constant. Non-ohmic devices can show curved V–I characteristics.

4. Resistance, Resistivity & Conductivity

R = ρL / A

Resistance of a uniform conductor.

ρ = RA / L

Resistivity. SI unit: Ω m.

σ = 1 / ρ

Conductivity. SI unit: S m⁻¹.

J = σE

Microscopic form of Ohm's law for a linear conductor.

E = ρJ

Equivalent form for a linear conducting material.

5. Temperature Dependence of Resistance

R = R₀[1 + α(T − T₀)]

Linear temperature relation over the range where the approximation is valid.

ρ = ρ₀[1 + α(T − T₀)]

Corresponding linear relation for resistivity when the same temperature coefficient applies.

For many metals, α is positive over the relevant temperature range, so resistance increases as temperature rises.

6. Electrical Energy & Power

P = VI

P = I²R

P = V² / R

Choose the form that matches the quantities given in the question.

W = Pt = VIt

Electrical energy transferred in time t for constant power.

7. Resistors in Series & Parallel

Series

R_eq = R₁ + R₂ + ...

Same current flows through every resistor in a single series path.

Parallel

1/R_eq = 1/R₁ + 1/R₂ + ...

The potential difference across parallel branches is the same.

8. Cell, EMF & Internal Resistance

V = ε − Ir

Terminal voltage of a discharging cell carrying current I through internal resistance r.

I = ε / (R + r)

Current in a simple circuit containing external resistance R and internal resistance r.

ε = V + Ir

Useful rearrangement during discharge.

When no current is drawn (I = 0), the terminal voltage equals the emf: V = ε.

9. Cells in Series & Parallel

Series

ε_eq = ε₁ + ε₂ + ...

r_eq = r₁ + r₂ + ...

For cells connected in series aiding, the emfs add.

Identical Cells in Parallel

ε_eq = ε

r_eq = r / n

For n identical cells connected in parallel, the emf remains equal to that of one cell while the equivalent internal resistance decreases.

10. Kirchhoff's Rules

ΣI = 0

Junction rule: algebraic sum of currents at a junction is zero; equivalently, total current entering equals total current leaving.

ΣΔV = 0

Loop rule: algebraic sum of potential changes around a closed loop is zero.

Crossing an element	Potential change
Cell from − to + terminal	+ε (rise)
Cell from + to − terminal	−ε (drop)
Resistor in direction of current	−IR
Resistor opposite to current	+IR

11. Wheatstone Bridge

P / Q = R / S

Balance condition, using the standard four-arm notation P, Q, R and S.

I_G = 0 at balance

No current flows through the galvanometer because its two junctions are at equal potential.

If the unknown resistance is S, then S = QR/P at balance.

12. High-Value Unit & Conversion Reminders

Quantity	SI unit	Useful identity
Current I	A	1 A = 1 C s⁻¹
Resistance R	Ω	1 Ω = 1 V A⁻¹
Resistivity ρ	Ω m	ρ = RA/L
Conductivity σ	S m⁻¹	σ = 1/ρ
Current density J	A m⁻²	J = I/A
Mobility μ	m² V⁻¹ s⁻¹	μ = vd/E
Power P	W	1 W = 1 J s⁻¹
Energy W	J	W = Pt

13. Formula Selection: Which Equation Should I Use?

• Given charge and time: I = ΔQ/Δt.
• Given microscopic carrier data: I = neAv_d.
• Given V and I: R = V/I and P = VI.
• Given wire dimensions and material: R = ρL/A.
• Given current and resistance: P = I²R.
• Given voltage and resistance: P = V²/R.
• Given a discharging cell: V = ε − Ir.
• Given a simple external circuit with a cell: I = ε/(R+r).
• Given a multi-loop circuit: use Kirchhoff's junction and loop rules.
• Given a balanced Wheatstone bridge: use the ratio condition and I_G = 0.

14. Last-Minute Exam Traps

• Do not confuse resistance with resistivity: resistance depends on dimensions; resistivity is a material property under specified physical conditions.
• Do not confuse current with current density: J includes area.
• For electrons, conventional current is opposite to electron drift direction.
• For a discharging cell, terminal voltage is ε − Ir, not ε + Ir.
• For identical cells in parallel, emf does not become nε.
• In a balanced Wheatstone bridge, the galvanometer current is zero.
• In Ohm's law questions, check whether physical conditions are constant.

Quick Revision Route

Learn: Notes → Practise: Important Questions + MCQs → Solve: Numericals + Case-Based → Test: Assertion–Reason → Next: Chapter Test.

Continue Current Electricity Preparation

Notes Important Questions MCQs Numericals Case-Based Questions Assertion–Reason Questions Chapter 1 Hub Chapter 2 Hub

Source note: The scope of this page follows the official CBSE 2026–27 Physics curriculum. The formula organization was cross-checked against current formula-sheet resources, but this page is original study material and should be used alongside the prescribed textbook and official CBSE documents.