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Current Electricity — Complete Theory, Formulas & Concepts

# Current Electricity — Complete Theory, Formulas & Concepts

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CBSE Class 12 Physics
NEET Physics
JEE Physics
Theory + Formula Revision

Current Electricity — Complete Theory, Formulas & Concepts

Master Current Electricity with clear theory, essential concepts,
important equations, circuit relationships, and high-yield formula
revision for CBSE Class 12, NEET and JEE Physics.

This page is the Theory & Formula reference
within the eduPhysics Current Electricity learning hub.

Current Electricity Learning Path:

Current Electricity Master Hub

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Theory & Formulas

Current Electricity: Quick Overview

Current Electricity deals with the motion of electric
charges through conductors and the physical laws used to describe
electric circuits. The chapter connects electric current, potential
difference, resistance, resistivity, cells, internal resistance,
combinations of resistors, electrical power, and Kirchhoff’s laws.

For exam preparation, the most important skill is not simply memorizing
formulas. You should understand what each quantity represents, when an
equation can be used, and how circuit conditions affect the result.

Core idea:
A potential difference establishes the conditions for charge flow.
Resistance opposes charge flow, while the current depends on the
electrical conditions of the complete circuit.

On this page:

  1. Electric Current
  2. Drift Velocity
  3. Current and Drift Velocity Relation
  4. Ohm’s Law
  5. Resistance
  6. Resistivity and Conductivity
  7. Effect of Temperature
  8. Resistors in Series
  9. Resistors in Parallel
  10. Cells, EMF and Terminal Voltage
  11. Internal Resistance
  12. Kirchhoff’s Laws
  13. Wheatstone Bridge
  14. Electrical Power and Energy
  15. Current Electricity Formula Sheet
  16. High-Yield Exam Tips

1. Electric Current

Electric current is the rate of flow of electric charge through a
cross-section of a conductor.

Current:
I = ΔQ / Δt

For a steady current:

I = Q / t
  • SI unit: ampere (A)
  • 1 ampere: 1 coulomb of charge passes through a cross-section per second.
  • Conventional current is taken in the direction of motion of positive charge.
  • In metallic conductors, electrons drift opposite to the conventional current direction.
Exam point:
Do not confuse electron flow with conventional current. In a metallic
conductor, electrons move opposite to the direction assigned to current.

2. Drift Velocity

In a conductor, free electrons undergo random thermal motion. When an
electric field is applied, the electrons acquire a small average
velocity called drift velocity.

Drift velocity:
vd = eEτ / m

where:

  • e = magnitude of electronic charge
  • E = electric field inside the conductor
  • τ = relaxation time
  • m = electron mass

The drift velocity of electrons is generally very small, even though
an electrical signal can be established through a circuit very quickly.

3. Current–Drift Velocity Relation

Consider a conductor of cross-sectional area A containing n free
electrons per unit volume. If the electrons have drift velocity
vd, the current is:

I = n e A vd

Therefore, current density is:

J = I/A = n e vd
Quantity Meaning SI Unit
I Electric current A
J Current density A m−2
n Number density of free electrons m−3
vd Drift velocity m s−1

4. Ohm’s Law

At constant physical conditions such as temperature, the current through
an ohmic conductor is directly proportional to the potential difference
across it.

V ∝ I

V = IR

Here R is the resistance of the conductor.

V–I Graph

For an ohmic conductor at constant temperature, the V–I graph is a
straight line passing through the origin. The slope of a V versus I
graph is the resistance.

R = V/I = slope of V–I graph
Important:
Ohm’s law is not universally valid for every electrical device.
Components such as diodes and filament lamps can have nonlinear
V–I characteristics.

5. Resistance

Resistance is the opposition offered by a conductor to the flow of
electric current.

R = V/I

Resistance depends on the nature and geometry of the conductor and,
for many materials, on temperature.

Factors Affecting Resistance

  • Length of conductor
  • Cross-sectional area
  • Material of conductor
  • Temperature
R = ρL/A
Change Effect on R
Length increases Resistance increases
Area increases Resistance decreases
Resistivity increases Resistance increases

6. Resistivity and Conductivity

Resistivity is an intrinsic property of a material that measures its
opposition to current flow. Unlike resistance, resistivity does not
depend on the dimensions of the particular conductor.

ρ = RA/L

R = ρL/A

  • SI unit of resistivity: Ω m
  • Resistivity depends on the material and temperature.
  • Resistance also depends on conductor dimensions.

Conductivity

σ = 1/ρ

The SI unit of conductivity is siemens per metre (S m−1).

7. Effect of Temperature on Resistance

For many metallic conductors over a moderate temperature range,
resistance increases approximately linearly with temperature.

RT = R0[1 + α(T − T0)]

Here α is the temperature coefficient of resistance at the reference
temperature.

  • Metals generally have a positive temperature coefficient.
  • Semiconductors generally show decreasing resistance with increasing temperature over appropriate ranges.

8. Resistors in Series

In a series combination, the same current flows through every resistor.

Req = R1 + R2 + R3 + …

The total potential difference is the sum of the potential drops:

V = V1 + V2 + V3 + …
Remember:
Series → same current → resistances add.

9. Resistors in Parallel

In a parallel combination, the potential difference across each
resistor is the same.


1/Req = 1/R1 + 1/R2 + 1/R3 + …

The total current is the sum of branch currents:

I = I1 + I2 + I3 + …
Remember:
Parallel → same voltage → conductances add.

Two Resistors in Parallel

Req = R1R2/(R1 + R2)

10. Cell, EMF and Terminal Voltage

A cell converts chemical energy into electrical energy and maintains a
potential difference in a circuit.

EMF

The electromotive force (emf), represented by ε, is the energy supplied
by the source per unit charge when the source transfers charge through
the complete internal circuit.

ε = W/q

Terminal Voltage

When a cell of emf ε and internal resistance r supplies current I to an
external circuit, the terminal potential difference is:

V = ε − Ir

This equation applies when the cell is delivering current to an external
load.

Common mistake:
EMF is not always equal to terminal voltage. A voltage drop Ir occurs
inside a real cell when current flows through its internal resistance.

11. Internal Resistance

A real cell has internal resistance, represented by r. It causes an
internal voltage drop when current flows.

V = ε − Ir

Therefore:

r = (ε − V)/I

Current Delivered by a Cell

If an external resistance R is connected to a cell of emf ε and internal
resistance r:

I = ε/(R + r)

Terminal Voltage

V = IR = εR/(R + r)

Short-Circuit Current

If the external resistance approaches zero:

Isc = ε/r
A short circuit can produce a very large current and may damage the
source or circuit. This is a theoretical limiting case in circuit
analysis, not a practical operating condition.

12. Kirchhoff’s Laws

Kirchhoff’s laws are essential for solving complex electrical networks
containing multiple loops, junctions, cells and resistors.

Kirchhoff’s Current Law — KCL

Kirchhoff’s first law follows from conservation of electric charge.
At any junction, the total current entering equals the total current
leaving.

ΣI = 0

Equivalently:

ΣIin = ΣIout

Kirchhoff’s Voltage Law — KVL

Kirchhoff’s second law follows from conservation of energy. The algebraic
sum of potential changes around any closed loop is zero.

ΣΔV = 0

Useful Sign Conventions

  • Choose a loop direction before writing the equation.
  • Across a resistor in the direction of assumed current: potential change is −IR.
  • Across a resistor opposite to assumed current: potential change is +IR.
  • Across a cell from negative to positive terminal: +ε.
  • Across a cell from positive to negative terminal: −ε.
Exam strategy:
You may assume current directions arbitrarily. If the calculated current
is negative, the actual direction is opposite to your assumption.

13. Wheatstone Bridge

A Wheatstone bridge can be used to compare resistances and determine an
unknown resistance.

At balance, no current flows through the galvanometer.

P/Q = R/S

If one resistance is unknown:

S = QR/P
Balance condition:
The bridge is balanced when the potentials at the two galvanometer
junctions are equal and the galvanometer current is zero.

14. Electrical Power and Energy

Electrical power is the rate at which electrical energy is transferred
or converted.

P = VI

Using Ohm’s law:

P = I²R = V²/R

Electrical Energy

W = Pt = VIt = I²Rt = V²t/R

The commercial unit of electrical energy is the kilowatt-hour (kWh).

1 kWh = 3.6 × 106 J

15. Current Electricity Formula Sheet

Use this section for rapid revision before a CBSE board examination,
NEET Physics practice session or JEE problem-solving session.

Concept Important Formula
Electric current I = Q/t
Current density J = I/A
Drift-current relation I = neAvd
Current density and drift velocity J = nevd
Ohm’s law V = IR
Resistance R = V/I
Resistance of a uniform conductor R = ρL/A
Resistivity ρ = RA/L
Conductivity σ = 1/ρ
Temperature dependence RT = R0[1 + α(T − T0)]
Series combination Req = R1 + R2 + …
Parallel combination 1/Req = 1/R1 + 1/R2 + …
Two resistors parallel Req = R1R2/(R1 + R2)
Cell current I = ε/(R + r)
Terminal voltage V = ε − Ir
Internal resistance r = (ε − V)/I
Short-circuit current Isc = ε/r
Kirchhoff’s current law ΣI = 0
Kirchhoff’s voltage law ΣΔV = 0
Wheatstone bridge balance P/Q = R/S
Electrical power P = VI = I²R = V²/R
Electrical energy W = Pt
Commercial energy unit 1 kWh = 3.6 × 106 J

16. Must-Know Comparisons

Pair Key Difference
EMF vs terminal voltage EMF is the source energy supplied per unit charge; terminal voltage is the potential difference available across the cell terminals under operating conditions.
Resistance vs resistivity Resistance depends on material and dimensions; resistivity is a material property at a specified temperature.
Series vs parallel Series: same current. Parallel: same potential difference.
Electron flow vs conventional current In metallic conductors, electron drift is opposite to conventional current direction.
Ideal vs real cell An ideal cell has zero internal resistance; a real cell has non-zero internal resistance.

17. Common Current Electricity Mistakes

  1. Using series resistance formulas for a parallel circuit.
  2. Forgetting that current is the same through series components.
  3. Forgetting that voltage is the same across parallel branches.
  4. Confusing resistance R with resistivity ρ.
  5. Using V = ε even when internal resistance causes a voltage drop.
  6. Mixing electron-flow direction with conventional-current direction.
  7. Using P = V²/R when the voltage is not the voltage across that particular resistor.
  8. Writing Kirchhoff loop equations without establishing a consistent sign convention.
  9. Ignoring units when converting mΩ, kΩ, μA, mA or μF-type quantities in numerical problems.

18. How to Solve Current Electricity Numericals

Step 1 — Identify

List the given quantities and identify exactly what the question
asks you to calculate.

Step 2 — Draw

Draw the circuit and label current directions, resistances,
potential differences and cells.

Step 3 — Choose

Select the governing relation: Ohm’s law, series/parallel reduction,
cell equation, KCL, KVL or power equation.

Step 4 — Solve

Substitute SI-compatible quantities and solve algebraically before
rounding the final result.

19. High-Yield Current Electricity Exam Tips

  • Memorize the difference between emf, terminal voltage, resistance and resistivity.
  • Know both series and parallel resistor formulas.
  • Be comfortable with I = neAvd.
  • Practice circuit questions involving internal resistance.
  • Use KCL for junction equations and KVL for loop equations.
  • Learn the Wheatstone bridge balance condition.
  • For power questions, select P = VI, I²R or V²/R according to the known quantities.
  • Always check whether the requested voltage is terminal voltage, emf or voltage across a particular component.
  • Check dimensions and units before finalizing numerical answers.

Current Electricity — 60-Second Revision

  • Current: I = Q/t
  • Ohm’s law: V = IR
  • Resistance: R = ρL/A
  • Drift current: I = neAvd
  • Series: Req = ΣR
  • Parallel: 1/Req = Σ(1/R)
  • Cell: I = ε/(R+r)
  • Terminal voltage: V = ε − Ir
  • KCL: ΣI = 0
  • KVL: ΣΔV = 0
  • Power: P = VI = I²R = V²/R

20. Continue Your Current Electricity Preparation

Current Electricity Master Hub

Explore the complete Current Electricity learning ecosystem:
theory, formulas, practice, numericals and exam resources.


→ Current Electricity Master Hub

Current Electricity — Exam Practice

Test your preparation with chapter-focused previous-year and
exam-oriented questions.


→ Current Electricity Exam Practice

Current Electricity MCQs

Practice conceptual and numerical MCQs after completing this
theory and formula revision page.

MCQ child page: add the link here after Child Page 2 is created.

Master Current Electricity Step by Step

Understanding Current Electricity becomes much easier when theory,
formulas, circuit reasoning and exam practice are studied together.
Use this page as your concept and formula reference, then move to
problem-solving and previous-year questions.


Start with the

Current Electricity Master Hub

and build your preparation from concept → formula → application →
exam practice.

21. Frequently Asked Questions — Current Electricity

What is electric current?

Electric current is the rate of flow of electric charge through a
cross-section of a conductor. For steady current, I = Q/t.

What is Ohm’s law?

At constant physical conditions, the potential difference across an
ohmic conductor is directly proportional to the current through it:
V = IR.

What is the formula for resistance?

For a uniform conductor, resistance is R = ρL/A, where ρ is resistivity,
L is length and A is cross-sectional area.

What is the difference between resistance and resistivity?

Resistance depends on both material and dimensions of a conductor,
whereas resistivity is an intrinsic material property at a specified
temperature.

What is the formula for current through a cell?

For a cell of emf ε, internal resistance r and external resistance R,
the current delivered is I = ε/(R+r).

What is Kirchhoff’s current law?

Kirchhoff’s current law states that the algebraic sum of currents at a
junction is zero, or equivalently, total current entering a junction
equals total current leaving it.

What is Kirchhoff’s voltage law?

Kirchhoff’s voltage law states that the algebraic sum of potential
changes around a closed loop is zero.

What is the formula for electrical power?

Electrical power can be written as P = VI, P = I²R or P = V²/R,
depending on the quantities known.

eduPhysics: This page is designed as a concept and
formula revision resource for CBSE Class 12, NEET and JEE Physics
preparation. Always verify the exact syllabus and examination pattern
applicable to your examination year.

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