The chapter's opening section, saved for last. Read it once, carefully — there is one genuinely counter-intuitive idea buried in it, and NEET does ask about it.
NCERT §3.2, §3.3 · Points to Ponder 1 · fully in syllabus · occasional definition or integration question
Part 1 · The idea, told simply
Current is a counting rate. Stand at a point in a wire and count how much charge goes past you each second. That number is the current.
Story track · the turnstile
Picture a turnstile at a station counting people through. Some people walk forward through it; occasionally someone doubles back the other way. What the station cares about is the net flow: forward minus backward.
NCERT sets current up exactly this way. Imagine a small area held across the flow. In a time t, let q₊ be the net positive charge that goes forward through it and q₋ the net negative charge that goes forward. The net charge carried forward is
q = q₊ − q₋ I = q/t
The minus sign is not a mistake. Negative charge going forward is equivalent to positive charge going backward, so it must be subtracted to get the net forward transport.
NCERT adds a neat aside: if the answer comes out negative, that simply means the current runs the other way. Same idea as a negative Kirchhoff current in Topic 6.
Animation 1 · Counting charge through an area
Positive charges forward, negative charges forward — and what the net current comes to.
When the current is not steady
Maths track · the general definition
The formula I = q/t assumes the flow is steady. When it is not, NCERT defines the current at an instant as a limit:
I(t) = lim (Δt → 0) ΔQ/Δt = dQ/dt
Reading this backwards gives the result that gets examined: the charge that has flowed in a time interval is the integral of the current, which is the area under the I–t graph.
q = ∫ I dt = area under the current–time graph
This is the standard trap in the topic. If the current is changing, you cannot simply multiply the current at one moment by the elapsed time — that would be like finding a distance by multiplying the starting speed by the time.
Animation 2 · Charge is the area under the curve
Drag the time limit. The shaded area is the charge that has passed — and it is not I × t unless the line is flat.
Part 2 · The counter-intuitive bit: current is a scalar
Current has a direction marked on the diagram — and it is still a scalar
Every circuit diagram draws current with an arrow. It is natural to conclude it must be a vector. It is not.
NCERT Points to Ponder 1 gives two reasons:
Currents do not obey the law of vector addition. Two currents meeting at a junction add algebraically — 3 A plus 4 A gives 7 A, whatever the angle between the wires. If current were a vector, wires meeting at 90° would give 5 A, which is simply wrong.
Its definition produces a scalar. The current through an area of cross-section is the scalar product of two vectors: I = j · ΔS. A scalar product of two vectors is a scalar.
The arrow on a circuit diagram is bookkeeping — it records the sense of flow along a wire, which is all you need when the flow is confined to a wire. The genuinely vector quantity here is the current density j.
Animation 3 · Why vector addition gives the wrong answer
Two wires meeting at a junction. Change the angle between them and watch what each rule predicts.
Part 3 · Why a steady current needs a battery
Story track · NCERT's cylinder
NCERT §3.3 runs a thought experiment worth following, because it explains why circuits need cells at all.
Take a metal cylinder. Stick a disc carrying +Q on one flat end and a disc carrying −Q on the other. A field is set up inside, pointing from the positive end to the negative. The free electrons feel a force and drift towards the +Q end.
So a current flows — briefly. As the electrons arrive, they neutralise the charges that created the field. The field dies, the drift stops, and the current ceases. NCERT's phrasing: there will be a current for a very short while and no current thereafter.
To get a steady current, something must keep replenishing the charges at the ends as fast as they are neutralised. That something is a cell or a battery. This is precisely the job Topic 2's emf does.
Animation 4 · A current that dies, and one that does not
Left: charged discs, neutralising. Right: the same cylinder with the charge replenished.
Part 4 · The ampere and the scale of things
The ampere is an SI base unit — it is not derived from anything else. NCERT notes that it is defined through the magnetic effects of currents, which belongs to Chapter 4 rather than this one. Charge is the derived quantity here: 1 coulomb is 1 ampere-second.
Situation
Typical current
Source
Currents in our nerves
microamperes
NCERT §3.2
Domestic appliances
of the order of an ampere
NCERT §3.2
An average lightning stroke
tens of thousands of amperes
NCERT §3.2
Animation 5 · Ten powers of ten of current
From a nerve impulse to a lightning strike, on a scale that fits them both.
Each mark is a factor of ten
Trap · the six that cost marks
Calling current a vector because it is drawn with an arrow. It is a scalar; j is the vector.
Adding currents at a junction as vectors. They add algebraically, whatever the angle.
Using I × t when the current is changing. Use the area under the I–t graph.
Forgetting the minus sign in q = q₊ − q₋. Negative charge going forward counts against the total.
Thinking charged discs alone can drive a steady current. The current dies as the charges neutralise.
Treating the ampere as a derived unit. It is an SI base unit; the coulomb is derived from it.
Part 5 · Formula sheet
Definition
Net charge carried forward: q = q₊ − q₋
Steady current: I = q/t
Instantaneous current: I(t) = lim(Δt→0) ΔQ/Δt = dQ/dt
Charge from a varying current: q = ∫ I dt = AREA under the I–t graph
A negative result simply means the current flows the other way
Scalar nature (Points to Ponder 1)
Current is a SCALAR, though represented with an arrow
Currents do NOT obey the law of vector addition
at a junction they add ALGEBRAICALLY, whatever the angle
I = j · ΔS a scalar product of two vectors → a scalar
The VECTOR quantity is the current density j, not I
Units and dimensions
Current I : unit ampere (A) · dimension [A] · SI BASE UNIT
Charge q : unit coulomb (C) = A s · dimension [T A]
1 A = 1 C s⁻¹
The ampere is defined through the magnetic effects of currents
Electrons per second for a current I: N = I/e
For I = 1 A: N = 1/(1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸ per second
Orders of magnitude (NCERT §3.2)
Nerve currents ≈ microamperes
Domestic appliances ≈ amperes
Average lightning ≈ tens of thousands of amperes
Currents in conductors (§3.3)
No field → random thermal motion, average velocity zero, NO net current
Charged discs on a cylinder → a brief current that dies as charges neutralise
Steady current requires the charges to be continuously replenished
→ that is the job of a cell or battery
Free charges occur naturally in the ionosphere
Bound electrons do not accelerate even when a field is applied
Sanity checks
Current is scalar · current density is vector
Junction currents add algebraically, never by the parallelogram law
Constant current → q = It
Varying current → q = ∫I dt, the area under the graph
The ampere is a base unit; the coulomb is derived
Part 6 · 50 NEET-pattern questions with full solutions
Includes 4 graph-based questions, 3 assertion–reason questions, and 8 tagged Scalar on the vector-versus-scalar distinction. Year labels are not attached: the patterns are authentic, the wording is mine.
Topic 12 of 12 — the set is complete
Tier 1: resistor networks, cells and internal resistance, drift velocity, resistivity and stretching. Tier 2: power and heating, Kirchhoff's rules, cells in series and parallel, the bridges. Tier 3: temperature dependence, materials, Ohm's law limits. Tier 4: this file. Next step is a mixed full-chapter test — and, more usefully, sending back the questions that were answered wrongly so the remediation can be aimed rather than guessed.