Topic 1 of 15 Unit-II · Current Electricity Class 12 · Punjab Board · PSEB

Electric Current

The directed rate of flow of electric charge through a conductor. From the absolute basics (what is charge?) all the way to the advanced microscopic picture — this page takes you from zero to hero on Topic 1.

SI unit
ampere (A)
Symbol
I
Equation
I = dQ/dt
Type
Scalar
On this page · 18 sections
SECTION 01

Executive Summary

In one paragraph

Electric current is the directed rate of flow of electric charge through a conductor. In metals, mobile free electrons carry the charge, but by convention the current is taken in the direction positive charges would move — opposite to electron motion.

The fundamental definition is I = dQ/dt, with SI unit ampere (A), where 1 A = 1 C/s. For a steady current, charge versus time is a straight line through the origin with slope equal to the current. Current is a scalar quantity; its companion current density J = I/A is a vector.

This topic asks you to master the definition and derivations, name the charge carriers in each kind of conductor, distinguish conventional from electron flow, and solve graded numerical problems on charge, time, and number of electrons.

SECTION 02

Topic Map

The five micro-topics this lesson breaks into. Each is covered in the theory section below.

/01

Definition of Current

Directed flow of charge; I = Q/t; SI unit ampere (A). Instantaneous form I = dQ/dt. Direction set by convention.

/02

Charge Carriers

In metals: free electrons. In electrolytes & ionised gases: positive and negative ions. In semiconductors: electrons and holes.

/03

Conventional vs Electron Flow

Conventional current is the direction of positive charge flow (arrow from + to −). Electrons drift in the opposite direction.

/04

Current Density

J = I/A, SI unit A/m². A vector quantity in the direction of conventional current. Same as the direction of E in a conductor.

/05

Relation to Drift

Preview: I = neAvd, where vd is drift speed. Detailed treatment in Topic 2 · Flow of Charges.

SECTION 03 · LEVEL ZERO

Prerequisites — Start Here

Before we touch any formula, make sure these five things are crystal clear. If any of them feels shaky, slow down and read it twice. The rest of the topic is built on top of these.

Pre-req 1 · What is electric charge?

Charge is a property of matter

Some particles have it; some don't. Protons have a tiny positive charge (+e). Electrons have an equal tiny negative charge (−e). Neutrons have zero charge. A whole atom is neutral because the number of electrons matches the number of protons.

The SI unit of charge is the coulomb (C). One coulomb is huge — it equals the charge of about 6.25 × 1018 electrons. So when you see "0.5 C of charge flowed", picture trillions and trillions of electrons.

Pre-req 2 · What is a conductor?

Some materials let charges move, others don't

In metals like copper, aluminium, and silver, one or two electrons per atom are not tightly bound — they can wander freely through the metal. These are called free electrons (or conduction electrons). Metals are called conductors because of these.

In materials like rubber, glass, plastic, and wood, every electron is tightly bound to its atom. These are insulators — charge cannot flow through them in normal conditions.

In between sit semiconductors (silicon, germanium) — they have some free carriers but far fewer than metals.

Pre-req 3 · What does "flow of charge" mean?

Charges move in response to a push

If you connect a metal wire to the two terminals of a battery, the battery creates a tiny push — an electric field — inside the wire. The free electrons feel this push and start moving toward the positive terminal of the battery.

This continuous one-way motion of charges is what we call electric current. No battery, no push, no current.

Think of water in a pipe. If both ends are at the same height, water doesn't flow. If you raise one end, water flows downhill. A battery is like the pump or the height difference — it sets up the conditions for charges to flow.

Pre-req 4 · What is a closed circuit?

Current needs a complete loop

For current to flow continuously, charges must have a complete path to travel along — from one terminal of the battery, through the wires and devices, back to the other terminal. This is called a closed circuit.

If there is any break in the path (an open switch, a broken wire), current stops immediately everywhere in the circuit. This is called an open circuit.

Why? Because charges cannot pile up at the broken end — they need to keep moving in a loop. The instant the loop breaks, the flow stops.

Pre-req 5 · What does "rate" mean in physics?

Rate = quantity per unit time

When we say "rate of flow", we mean "how much per second". If 10 coulombs flow past in 2 seconds, the rate is 10/2 = 5 coulombs per second. We call this 5 amperes.

So "current is the rate of flow of charge" is shorthand for: current measures how many coulombs of charge cross any cross-section of the wire every second. That single sentence is the heart of this entire topic.

Ready?

If those five ideas feel solid, you are ready for the main theory below. If anything is fuzzy, read it one more time before moving on. From here it gets formal.

SECTION 04 · CORE THEORY

Theory and Key Formulas

Read each sub-section in order. Eight blocks cover everything the Punjab Board can ask on this topic.

4.1 — Definition of Electric Current

Electric current is the rate of flow of electric charge across any cross-section of a conductor. If a net charge ΔQ passes through a cross-section in time Δt, the average current is:

Average current
I = ΔQ / Δt
where Q is in coulombs, t is in seconds

For a smoothly varying charge Q(t), the instantaneous current is the time derivative:

Instantaneous current
I = dQ/dt
strict mathematical definition

For a steady current (constant in time), both reduce to the simple form I = Q/t. The SI unit is the ampere (A), where 1 A = 1 C / 1 s.

4.2 — Charge Carriers in Different Materials

Current is the flow of any charge carrier — not just electrons. The specific carriers depend on the conducting medium:

  • Metals (Cu, Al, Fe, Ag): conduction is by free electrons. One or two valence electrons per atom are not bound to any single atom; they drift through the lattice.
  • Electrolytes (NaCl solution, dilute H₂SO₄): both positive ions (cations) like Na+ and negative ions (anions) like Cl move in opposite directions. Both contribute to current.
  • Ionised gases / plasma (neon lamp, lightning, fluorescent tube): electrons and positive ions both move.
  • Semiconductors (Si, Ge): electrons in the conduction band and "holes" in the valence band. Detailed treatment in Chapter 14.
  • Vacuum (CRT, vacuum tube): only free electrons travelling through evacuated space.
Board-answer phrasing

When asked to identify the charge carrier, always state both the carrier type and the material — for example: "In an electrolyte, the charge carriers are positive ions (cations) and negative ions (anions), which move in opposite directions."

4.3 — Conventional Current vs Electron Flow

This is the single most confusing point in this topic.

Before the electron was discovered (1897), Benjamin Franklin had already established the convention that current flows from the positive terminal of a battery to the negative terminal in the external circuit — this is the conventional current. Decades later we learned that the actual charge carriers in metals are negatively charged electrons, which flow in the opposite direction (from − to +).

Conventional Current

Direction: from + terminal to − terminal (external circuit).

Sign: positive.

Used in: all problems, formulas, and circuit diagrams.

Electron Flow

Direction: from − terminal to + terminal — opposite to conventional current.

Physically real: yes, but not used in equations.

Why: historical convention, kept for consistency.

Common mistake

Students often draw the current arrow in the same direction as electrons. Always draw conventional current from + to − in the external circuit — opposite to electron motion.

4.4 — Current Density

Electric current is a scalar describing the total rate of charge flow through a conductor. Current density J is the corresponding vector quantity that describes the flow at a point.

Current density
J = I / A
SI unit: ampere per square metre (A/m²)

J is a vector in the direction of conventional current flow at that point (i.e., the direction in which positive charge would move under the local electric field). For a uniform conductor, the magnitude is just I/A and the direction is along the wire.

The relation between current density and electric field is given by the microscopic form of Ohm's law: J = σE, where σ is the conductivity of the material. (Covered in detail in Topic 8.)

4.5 — Charge Continuity (Same Current at All Cross-sections)

In a steady-state series circuit with a uniform conductor, the current is the same at every cross-section. This follows directly from conservation of electric charge: charge cannot accumulate at any cross-section in steady state, so what flows in must flow out.

This is why an ammeter placed at any point in a series circuit shows the same reading — at the start of the wire, in the middle, or at the end. It is also why thin and thick wires in series carry the same current despite different cross-sections (and therefore have different current densities J = I/A).

4.6 — Why Current is a Scalar Quantity

Current has a direction — we draw arrows in circuit diagrams — so why is it called a scalar?

The answer: currents do not follow vector addition. Consider a junction where two wires meet at right angles, each carrying 1 A. By vector addition, the resultant would be √2 ≈ 1.41 A at 45°. But experimentally, the total current leaving the junction is exactly 1 + 1 = 2 A — algebraic addition, governed by Kirchhoff's junction rule.

So we have:

  • Current (I): scalar — adds algebraically at junctions
  • Current density (J = I/A): vector — direction along charge flow at each point
Key insight

The direction of current is defined along the conductor, not in 3D space. That constraint is why current does not need vector addition.

4.7 — Alternate Form: Orbiting Charge

A useful extension: if a charge Q is moving in a closed loop and completes f revolutions per second, the equivalent steady current is:

Current from orbiting charge
I = Q × f = Q / T
where T = 1/f is the period of revolution

This form is used in atomic-model problems where an electron orbits a nucleus, and in cyclotron physics. It is the same definition I = Q/t applied to a periodic system.

4.8 — Microscopic Form (Hero Level)

So far we have defined current macroscopically — total charge crossing a section per unit time. There is a deeper expression in terms of what individual electrons are doing:

Microscopic form
I = n e A vd
n = number density of free electrons; A = cross-section area; vd = drift velocity

This formula is derived in detail in Topic 2 — Flow of Charges in a Metallic Conductor. For now, notice that current is set by:

  • How many free electrons there are (n, the carrier density — about 8.5 × 10²⁸ per cubic metre in copper),
  • How fat the wire is (A, the cross-section), and
  • How fast they drift on average (vd, typically ~10⁻⁴ m/s in copper).

Even though electrons drift extremely slowly, the wire carries useful current because n is enormous — there are trillions of trillions of free electrons in every cubic centimetre of metal.

SECTION 05

Visual Notes

Complete revision poster for all 15 topics of Unit-II. Section 1 covers this topic. Tap to enlarge.

Unit-II Current Electricity complete revision notes — all 15 topics in one poster
Tap to enlarge · Print at A4 size and keep on your study wall · Reference back as you move through topics 2–15
SECTION 06

Sample Derivation

Step-by-step derivation of the instantaneous form, with an applied numerical example.

Step 1 — Start from the definition. If a net charge ΔQ passes through a cross-section in time Δt, then the average current over that interval is:

Iavg = ΔQ / Δt

Step 2 — Take the limit for instantaneous current. For a continuously varying charge Q(t), shrink the interval Δt to zero:

I = limΔt→0 (ΔQ/Δt) = dQ/dt

Step 3 — Apply to a numerical case. Suppose 720 C of charge passes through a wire in 4.00 s of steady flow.

Working
I = ΔQ / Δt = 720 / 4.00

So I = 180 A.

Why this derivation matters

This is the basis of everything else in the unit. The instantaneous form I = dQ/dt is what lets us handle circuits where current changes with time — capacitor charging, AC circuits, transient discharges.

SECTION 07

Typical Graphs

Two standard plots every student must recognise at sight.

(a) Charge versus Time — Q vs t

For a constant current I, the charge accumulated since t = 0 is Q(t) = I·t + Q₀, which is a straight line on a Q-t plot.

  • The slope of the Q-t graph equals the current: slope = dQ/dt = I.
  • If the graph passes through the origin, Q₀ = 0.
  • A horizontal Q-t line means no current is flowing (no charge is accumulating).
  • A curved Q-t line means current is changing with time (the slope changes from point to point).

(b) Current versus Time — I vs t

  • For steady DC: I(t) is a horizontal line at the value of I.
  • For AC (Chapter 7): I(t) is a sine curve oscillating between +I₀ and −I₀.
  • For a charging capacitor: I(t) decays exponentially from a maximum value to zero.
  • For a discharging capacitor: same exponential decay shape.
Graph reading tip

On any I vs t graph, the area under the curve between time t₁ and t₂ gives the total charge transferred during that interval: Q = ∫I dt.

SECTION 08

Worked Numericals

Eight graded problems — from absolute basics to advanced. Each solution uses the 5-line format expected in board answers: Given → To find → Formula → Calculation → Answer.

Easy · 1 mark
Q1. If a charge of 12 C flows through a wire in 3 s, find the current.
Given: Q = 12 C; t = 3 s
To find: Current I
Formula: I = Q/t
Calculation: I = 12/3 = 4 A
Answer: I = 4 A
Easy · 2 marks
Q2. If 1.6 × 10¹⁹ electrons cross a section of a wire in 4 seconds, find the current.
Given: n = 1.6 × 10¹⁹ electrons; t = 4 s; e = 1.6 × 10⁻¹⁹ C
To find: Current I
Formula: Q = ne ; I = Q/t
Calculation: Q = 1.6 × 10¹⁹ × 1.6 × 10⁻¹⁹ = 2.56 C ; I = 2.56/4 = 0.64 A
Answer: I = 0.64 A
Easy · 2 marks
Q3. A current of 5 A flows in a circuit for 2 minutes. Calculate (a) the total charge transferred and (b) the number of electrons.
Given: I = 5 A; t = 2 min = 120 s
To find: (a) Q, (b) n
Formula: Q = It; n = Q/e
Calculation: (a) Q = 5 × 120 = 600 C; (b) n = 600 / (1.6 × 10⁻¹⁹) = 3.75 × 10²¹
Answer: Q = 600 C; n = 3.75 × 10²¹ electrons
Medium · 2 marks · Conventional vs electron direction
Q4. In a copper wire, 5 × 10¹⁸ electrons pass a point in 2 s. What is the conventional current, and in which direction?
Given: n = 5 × 10¹⁸; t = 2 s; e = 1.6 × 10⁻¹⁹ C
To find: I and its direction
Formula: Q = ne; I = Q/t
Calculation: Q = 5 × 10¹⁸ × 1.6 × 10⁻¹⁹ = 0.8 C; I = 0.8/2 = 0.4 A
Answer: I = 0.4 A; conventional current is opposite to electron motion — toward the positive terminal of the source.
Medium · 3 marks · Current density
Q5. A copper wire of cross-sectional area 2 × 10⁻⁶ m² carries a current of 4 A. Find the current density.
Given: I = 4 A; A = 2 × 10⁻⁶ m²
To find: Current density J
Formula: J = I/A
Calculation: J = 4 / (2 × 10⁻⁶) = 2 × 10⁶ A/m²
Answer: J = 2 × 10⁶ A/m² (directed along the conventional current)
Medium · 3 marks · Multi-carrier
Q6. In a hydrogen discharge tube, 3.13 × 10¹⁸ electrons and 1.5 × 10¹⁸ protons cross a given cross-section per second, moving in opposite directions. Find the net current.
Given: n_e = 3.13 × 10¹⁸/s; n_p = 1.5 × 10¹⁸/s; e = 1.6 × 10⁻¹⁹ C
Concept: Both carriers contribute current in the same direction (positive charges going one way and negative charges going the opposite way both produce conventional current in the same sense).
Formula: I = (n_e + n_p) × e
Calculation: I = (3.13 + 1.5) × 10¹⁸ × 1.6 × 10⁻¹⁹ = 4.63 × 10¹⁸ × 1.6 × 10⁻¹⁹ ≈ 0.741 A
Answer: I ≈ 0.74 A
Hard · 3 marks · Drift velocity preview
Q7. A copper wire of cross-sectional area A = 1 × 10⁻⁶ m² carries a current of I = 3 A. The free electron density in copper is n = 8.5 × 10²⁸ per m³. Find the drift velocity of electrons.
Given: I = 3 A; A = 1 × 10⁻⁶ m²; n = 8.5 × 10²⁸ /m³; e = 1.6 × 10⁻¹⁹ C
To find: Drift velocity vd
Formula: I = neAvd → vd = I/(neA)
Calculation: vd = 3 / (8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 10⁻⁶) ≈ 2.2 × 10⁻⁴ m/s
Answer: vd ≈ 2.2 × 10⁻⁴ m/s (~0.2 mm per second — very slow!)
Hard · 3 marks · Time-varying current
Q8. The current through a wire varies with time as I(t) = (4 + 2t) A, where t is in seconds. Find the total charge that flows through the wire in 5 seconds.
Given: I(t) = 4 + 2t A; t from 0 to 5 s
To find: Total charge Q in 5 s
Formula: Q = ∫I dt (because current is variable)
Calculation: Q = ∫05(4 + 2t)dt = [4t + t²]05 = (20 + 25) − 0 = 45 C
Answer: Q = 45 C
SECTION 09

Common Mistakes

Six errors that cost marks in every board exam. Learn them in advance.

Mistake 1 · Reversing the direction

Forgetting that electrons are negative and so drawing the current arrow in the direction of electron motion. Always use conventional direction — current arrow from + to − in the external circuit.

Mistake 2 · Unit mismatch

Mixing amperes, coulombs, and seconds without checking. Always confirm: 1 A = 1 C/s. If t is given in minutes, multiply by 60 before using it in I = Q/t.

Mistake 3 · Mixing Q and I

Writing Q = I/t instead of Q = I × t. Remember: I = ΔQ/Δt, so Q = I × t — never the other way around.

Mistake 4 · Graph misreading

Thinking constant accumulated charge means zero current. Wrong direction — a flat Q-t line means no charge is being added per second, so I = dQ/dt = 0. A steady current shows up as a linearly rising Q-t line.

Mistake 5 · Vector treatment

Trying to add currents using the vector triangle law at junctions. Current is a scalar — add algebraically (Kirchhoff's junction rule). Only current density J is a vector.

Mistake 6 · Carriers in electrolytes

Saying current in an electrolyte is "only due to electrons" or "only due to ions". In an electrolyte both positive ions (cations) and negative ions (anions) move, and both contribute to current in the same direction.

SECTION 10

Glossary — 28 Terms

Every term that may appear in board questions on this topic, with a one-sentence definition.

Electric current
Rate of flow of electric charge across any cross-section of a conductor.
Ampere (A)
SI unit of electric current; 1 A = 1 coulomb of charge passing per second.
Coulomb (C)
SI unit of electric charge; equal to the charge of 6.25 × 10¹⁸ electrons.
Conventional current
Current direction taken as the direction in which positive charges would move; from + to − in external circuit.
Electron flow
Actual direction of electron motion in a metal; from − to + terminal, opposite to conventional current.
Charge carrier
Any charged particle (electron, ion, hole) that physically carries charge through a material.
Free electron
A valence electron loosely bound in a metal lattice that can drift through the metal under an electric field.
Cation
A positively charged ion that has lost one or more electrons; moves toward cathode in electrolysis.
Anion
A negatively charged ion that has gained one or more electrons; moves toward anode in electrolysis.
Hole
In a semiconductor, the absence of an electron in the valence band; behaves as a positive charge carrier.
Charge quantization
Principle that all observable charges are integer multiples of the elementary charge e.
Elementary charge (e)
Magnitude of charge on an electron or a proton; e = 1.6 × 10⁻¹⁹ C.
Current density (J)
Current per unit cross-sectional area; vector quantity with direction along conventional current; SI unit A/m².
Drift velocity (vd)
Average velocity acquired by free electrons in a conductor under an applied electric field; typically ~10⁻⁴ m/s in copper.
Scalar quantity
A physical quantity that has magnitude only, no vector direction following addition laws.
Vector quantity
A physical quantity that has both magnitude and direction, following vector addition rules.
SI unit
International System unit; the standard agreed-upon measurement units used in physics.
Dimensional formula
Expression showing how a physical quantity relates to fundamental SI dimensions (M, L, T, A, K, mol, cd).
Steady current
Current that does not change with time; constant magnitude and direction.
Instantaneous current
Current at a specific instant for a time-varying flow; I = dQ/dt.
Direct current (DC)
Current that flows in one direction only with constant magnitude; produced by cells and batteries.
Alternating current (AC)
Current whose magnitude and direction change periodically with time; produced by generators; mains supply.
Open circuit
A circuit with at least one break in the conducting path; no current flows.
Closed circuit
A circuit forming a complete conducting loop; current can flow continuously.
Junction (node)
Point in a circuit where three or more conductors meet; currents add algebraically by Kirchhoff's rule.
Electrolyte
A liquid (usually a salt or acid solution) that conducts electricity through ion movement.
Plasma
An ionised gas containing free electrons and positive ions; conducts electricity (e.g., neon tubes, lightning, stars).
Conductor / Insulator
Conductor: material with many free carriers (e.g., metals). Insulator: material with negligible free carriers (e.g., glass, rubber).
SECTION 11

PSEB / Board Focus

What the Punjab School Education Board typically asks on this topic and how to score full marks.

Typical question types in the Punjab Board exam

  • 1-mark MCQ / Assertion-Reasoning: definition of ampere; identification of charge carriers; scalar nature of current.
  • 2-mark short answer: definition + SI unit + dimensional formula; distinguish conventional vs electron flow; identify carriers in different media.
  • 3-mark numerical: compute current given charge & time, or number of electrons & time; sometimes combined with drift velocity preview.
  • 5-mark long answer: usually combined with drift velocity, mobility, or Ohm's law (Topics 2, 3, 4) as part of a longer derivation.
Pro tip for board answers

When asked to define electric current, always state three things together: (1) the qualitative definition ("rate of flow of charge"), (2) the formula (I = dQ/dt), and (3) the SI unit (ampere = 1 C/s). This earns full marks even for a 1-mark question.

Diagram practice

Many board questions ask for a labelled diagram of conventional vs electron flow. Practice drawing a battery + wire loop + arrow for conventional current (from +) + arrow in opposite direction for electron flow. A clean diagram alone earns 1 mark in a 2-mark question.

SECTION 12

Past Board Questions

Board-pattern questions on this topic with model answers. Compare your attempt with the model.

SECTION 13 · LARGEST PRACTICE SET

Practice MCQs · 50 Questions

50 questions covering every sub-topic — definitions, numericals, conventional vs electron flow, charge carriers, current density, and junctions. Tap an option to check.

Correct
0
Attempted
0
Total
50
SECTION 14

Fill in the Blanks · 15

Complete each statement with the correct word, phrase, or value.

SECTION 15

Match the Columns

Pair each item in Column A with the correct entry in Column B.

Column A

A. I = dQ/dt
B. J = I/A
C. 1.6 × 10⁻¹⁹ C
D. I = neAvd
E. I = Q × f

Column B

1. Microscopic form of current
2. Equivalent current of an orbiting charge
3. Magnitude of the elementary charge
4. Current density (vector)
5. Instantaneous current
✓ Answers: A → 5; B → 4; C → 3; D → 1; E → 2
SECTION 16

True or False · 10

State whether each statement is true (T) or false (F). Answers are shown beside each statement.

1. Electric current is a vector quantity.
FALSE
2. Conventional current flows from + to − in the external circuit.
TRUE
3. Electrons in a metal wire flow from + to − terminal externally.
FALSE
4. SI unit of current density is A/m².
TRUE
5. In a metallic conductor, holes are the main charge carriers.
FALSE
6. In a steady-state series circuit, the current is the same at all cross-sections.
TRUE
7. At a circuit junction, currents add vectorially using the triangle law.
FALSE
8. Current density J is a vector quantity directed along the conventional current.
TRUE
9. 1 ampere is equal to 1 coulomb per second.
TRUE
10. Current can flow in an open circuit.
FALSE
SECTION 17

Short Answer Questions · 12

1–2 mark questions. Each comes with a concise model answer suitable for direct reproduction in board exams.

SECTION 18

Long Answer Questions · 6

3–5 mark questions requiring derivations, comparisons, or detailed explanations.

SECTION 19

Assertion-Reasoning · 5

Each item has an Assertion (A) and a Reason (R). Choose: (a) Both A and R are true, and R is correct explanation of A. (b) Both true, R is NOT correct explanation. (c) A true, R false. (d) A false, R true.

SECTION 20

Higher-Order Thinking · Punjab Context

Three questions that take the basic concept of current and apply it to situations you see every day in Kassoana, Ferozepur, and across Punjab.

HOTS 1 · Domestic wiring

In a farmhouse near Kassoana, the main electricity supply line carries about 30 A during peak summer when the AC, fridge, fans, and tubewell motor all run together. (a) How many electrons flow through the main switch in 1 second? (b) If a stray cat brushes against an exposed live wire and 50 mA flows through its body for 0.2 seconds, how many electrons pass through? (c) Why is even a small current dangerous for living beings even though the total charge is tiny? (Hint: use Q = ne, then think about what electricity does to nerves and muscles)

HOTS 2 · Lightning over Ferozepur

During monsoon thunderstorms over Ferozepur, lightning can deliver up to 30,000 A in a flash that lasts only 30 microseconds. (a) Calculate the total charge transferred in one lightning bolt. (b) Compare this with the charge passing through a 60 W bulb in 1 hour (assume 220 V supply, so I = 60/220 = 0.27 A). (c) Why does lightning cause more damage than a bulb running for hours, when the total charge might be similar? (Think about: rate of energy transfer and what it does to materials)

HOTS 3 · Punjab tubewell circuits

Wheat farmers across Punjab rely on electric tubewells to pump groundwater. A typical 5 HP submersible pump draws a steady current of 7 A from a 415 V three-phase line. (a) How much charge does it move per second? (b) If the pump runs 6 hours per day during kharif season, how many electrons have flowed through it in 30 days? (c) Express the daily charge transferred in terms of multiples of "1 coulomb" — and explain why this is such a huge number but the bulb at your home still works on the same kind of charge. (Concept: charge per second is the rate; total charge over time is the integral)

SECTION 21

One-Page Revision Map

The entire topic compressed into a single table. Memorise this and you can answer 80% of board questions on Electric Current.

AspectKey Point
DefinitionRate of flow of charge: I = ΔQ/Δt. SI unit: ampere (A); 1 A = 1 C/s.
Instantaneous formI = dQ/dt for variable charge flow.
Charge carriersMetals: free electrons. Electrolytes: cations and anions. Semiconductors: electrons and holes. Plasma: electrons and ions.
DirectionConventional current: from + to − (direction positive charge would move). Electron flow: opposite, from − to +.
Type of quantityScalar. Adds algebraically at junctions (Kirchhoff's rule). Current density J = I/A is the corresponding vector.
ContinuityIn steady state, current is the same at all cross-sections of a uniform series conductor.
Q vs t graphStraight line for steady current; slope = I.
I vs t graphHorizontal for DC; sinusoidal for AC; exponential decay for charging/discharging capacitor.
Microscopic formI = neAvd (covered in detail in Topic 2 — Flow of Charges).
Orbital formI = Q × f for a charge revolving with frequency f (Bohr atom, cyclotron).
Charge quantizationQ = n × e, where n is an integer and e = 1.6 × 10⁻¹⁹ C.
Common mistakesReversing direction; mixing units; writing Q = I/t; treating I as vector; ignoring ion contribution in electrolytes.
SECTION 22

Formula Sheet

Every formula from this topic, with meaning and units. Print this page and stick on your study wall.

FormulaMeaning / Units
I = Q/tSteady current = charge per unit time. SI unit: ampere (A).
I = dQ/dtInstantaneous current for time-varying charge. Unit: ampere.
Q = ∫ I dtTotal charge from variable current. Integrate I(t) between time limits.
Q = I × tCharge transferred in time t at steady current I. Unit: coulomb (C).
Q = n × eCharge quantization: n electrons × elementary charge (e = 1.6 × 10⁻¹⁹ C).
J = I / ACurrent density (vector). SI unit: A/m².
I = neAvdMicroscopic form using drift velocity (Topic 2).
I = Q × f = Q / TEquivalent current of a charge revolving with frequency f (used in Bohr atom).
1 A = 1 C/sSI definition of ampere.
[I] = [A]Dimensional formula of current. Current is a base SI quantity.