NDA Physics · Electricity and Magnetism

Electric Current and Ohm's Law

Electric current is the rate of flow of charge (I = Q/t); in a metal it is carried by free electrons, and for an ohmic conductor the current is proportional to the applied voltage (V = IR).

All Electricity and Magnetism notes NDA Physics strategy

Why this matters

This is the gateway to every circuit problem in the chapter — 9 PYQs covering the definition of current (Q = It is asked almost every year), what carries it in a metal, Ohm's law V = IR, the ohmic/non-ohmic split, and AC vs DC. Nail Q = It and V = IR here and the power, resistance, and network subtopics become arithmetic.

Concept 1 of 5

Electric current as rate of flow of charge

Intuition

Current measures how much charge passes a point each second. If 1 coulomb flows past every second, that is 1 ampere. Over a time t, the total charge delivered is simply current × time.

Definition

Electric current is the rate of flow of charge: $I = Q/t$ . The SI unit is the ampere (1 A = 1 C/s). Rearranged, the charge transported in time $t$ is $Q = It$ . Conventional current is taken in the direction a POSITIVE charge would move — opposite to the actual electron drift in a metal.

Current and charge

I = \dfrac{Q}{t} \quad\Longleftrightarrow\quad Q = I\,t

Icurrent (ampere)
Qcharge (coulomb)
ttime (second)

Worked example

A current of 2 A flows through a wire for 5 minutes. How much charge passes through it?

Use $Q = It$ ; convert time to seconds: $5\text{ min} = 300$ s.
$Q = 2 \times 300 = 600$ C.

Answer:600 C.

Practice this conceptself-check · 3 quick reps

Try it yourself

How long must a 0.5 A current flow to deliver 90 C of charge?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Charge delivered by 3 A in 2 minutes?
2.
1 ampere equals how many coulombs per second?
3.
A 0.6 A current flows for 10 minutes. Charge?

From the bank · past-year question

Example 1Electricity and MagnetismEASY

A current of

0 \cdot 6

A is drawn by an electric bulb for 10 minutes. Which one of the following is the amount of electric charge that flows through the circuit?

[Q99 · Sep · 2022]

Convert minutes to seconds first

Q = It needs t in SECONDS. The dominant wrong answer forgets the ×60: 0.6 A × 10 = 6 (using minutes) instead of 0.6 × 600 = 360 C. Always convert time to seconds before multiplying.

Drill 2 more on electric current as rate of flow of charge

Concept 2 of 5

What carries current in a metal — free electrons

Intuition

A metal is a lattice of fixed positive ions in a 'sea' of loosely bound electrons. Those FREE electrons drift when a voltage is applied — they are the charge carriers. The ions stay put; they only vibrate.

Definition

In a metallic conductor, current is carried by free (conduction) electrons — not ions, not protons, not bound electrons. When a potential difference is applied, these electrons drift opposite to the field; the conventional current points the other way (direction of positive-charge flow).

Worked example

In a copper wire carrying current, which particles actually move, and in which direction relative to the conventional current?

Copper is a metal — the charge carriers are its free electrons.
Electrons are negative, so they drift TOWARD the higher potential, opposite to the field.
Conventional current is defined as the direction positive charge would flow — the OPPOSITE of electron drift.

Answer:Free electrons move; they drift opposite to the conventional current.

Practice this conceptself-check · 3 quick reps

Try it yourself

Why is an ionic solution able to conduct current, while a copper wire does so without any ions moving?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
What carries current in a metal?
2.
Conventional current direction vs electron drift?
3.
Do the metal ions move along the wire when current flows?

From the bank · past-year question

Example 2Electricity and MagnetismEASY

Which one of the following is primarily responsible for conduction of current in a metal ?

[Q133 · Apr · 2024]

Free electrons, not 'both bound and free'

Bound electrons stay with their atoms and don't conduct. The carriers are the FREE electrons only. 'Ions' is correct for solutions/gases, not for a solid metal.

Concept 3 of 5

Ohm's law — V = IR

Intuition

For an ordinary conductor at fixed temperature, push twice as hard (double the voltage) and twice as much current flows. The constant of proportionality is the resistance. On an I–V graph, an ohmic conductor is a straight line through the origin whose slope is 1/R.

Definition

Ohm's law: at constant temperature, the current through a conductor is directly proportional to the potential difference across it, $V = IR$ , where $R$ is constant. It is an empirical law, not a universal one — it holds for metals in a normal range, but NOT for all materials or arbitrarily strong fields. On an I–V plot (I vertical, V horizontal) an ohmic conductor is a straight line through the origin with slope $1/R$ — so a steeper line means a smaller resistance.

Ohm's law

V = I\,R

Vpotential difference (volt)
Icurrent (ampere)
Rresistance (ohm, Ω)

Worked example

A resistor carries 2 A when 10 V is applied. What current flows when the voltage is raised to 25 V (temperature unchanged)?

Find R first: $R = V/I = 10/2 = 5\,\Omega$ .
At 25 V: $I = V/R = 25/5 = 5$ A.
(Or directly: current scales with voltage, ×2.5, so 2 A → 5 A.)

Answer:5 A.

Practice this conceptself-check · 4 quick reps

Try it yourself

An electric heater draws 0.5 A at 220 V. What is its resistance, and how much current would it draw at 110 V?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
State Ohm's law as a formula.
2.
An I–V graph that is steeper corresponds to a larger or smaller resistance?
3.
12 V across 4 Ω drives what current?
4.
Is Ohm's law obeyed by all materials at all field strengths?

From the bank · past-year question

Example 3Electricity and MagnetismEASY

The potential difference between the two end terminals of an electric heater is 220 V and the current through it is 0·5 A. What would be the current through the heater if the potential difference across the terminals of the heater is reduced to 120 V?

[Q53 · Sep · 2023]

Ohm's law is NOT universal

The false statement the bank tests: 'all homogeneous materials obey Ohm's law irrespective of whether the field is within range or strong.' Wrong — Ohm's law is an empirical approximation that fails for non-ohmic materials and very strong fields.

Drill 2 more on ohm's law — v = ir

Concept 4 of 5

Ohmic vs non-ohmic conductors

Intuition

An ohmic device keeps the same resistance whatever the voltage — its I–V graph is a straight line. A non-ohmic device (like a diode or a bulb filament) changes resistance with conditions, so its I–V graph bends.

Definition

Ohmic — obeys $V = IR$ with constant $R$ ; I–V graph is a straight line through the origin. Examples: copper wire, nichrome heating coil, rheostat (a variable resistor, but ohmic).
Non-ohmic — $R$ depends on voltage/current/direction; I–V graph is curved or asymmetric. Example: a semiconductor diode (conducts one way, blocks the other).

An ohmic conductor is a straight line through the origin with slope 1/R — a steeper line means a smaller resistance. A curved trace is non-ohmic.

Worked example

Of a copper coil, a nichrome heating element, a rheostat, and a semiconductor diode, which one is non-ohmic?

Copper coil — metal, constant R → ohmic.
Nichrome heating element — a metal alloy resistor → ohmic.
Rheostat — a variable resistor, but each setting is ohmic → ohmic.
Semiconductor diode — conducts in one direction only, R depends on polarity → NON-ohmic.

Answer:The semiconductor diode is non-ohmic.

Practice this conceptself-check · 3 quick reps

Try it yourself

Device X has a straight-line I–V graph through the origin; device Y's I–V graph is a curve. Which obeys Ohm's law, and what does that say about each one's resistance?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
What shape is an ohmic conductor's I–V graph?
2.
Give a common non-ohmic device.
3.
Is a rheostat ohmic or non-ohmic?

From the bank · past-year question

Example 4Electricity and MagnetismEASY

Which one of the following devices is non-ohmic?

[Q60 · Apr · 2018]

A rheostat is ohmic; a diode is not

Students wrongly call a rheostat non-ohmic because it 'varies'. It varies the resistance VALUE by sliding a contact, but at any setting it obeys V = IR. The genuine non-ohmic device in the option list is the semiconductor diode.

Concept 5 of 5

Alternating current vs direct current

Intuition

Direct current flows one steady way (a battery). Alternating current reverses direction over and over — Indian mains runs at 50 Hz, so it completes 50 full back-and-forth cycles each second. A full cycle has two direction reversals, so it switches direction every 1/100 of a second.

Definition

DC flows in one direction (battery, cell). AC periodically reverses direction (mains supply). Indian mains frequency is 50 Hz — 50 complete cycles per second. Because each cycle reverses direction twice, the current changes direction every $\tfrac{1}{2\times50} = \tfrac{1}{100}$ second.

Property	DC	AC
Direction	Constant (one way)	Reverses periodically
Source	Cell / battery / DC generator	AC generator / mains
Indian mains frequency	—	50 Hz (reverses every 1/100 s)Q NDA 2024 Sep — mains changes direction every 1/100 s, NOT 1/50 s: a 50 Hz cycle reverses TWICE per cycle.
Transformable?	No (transformers need changing flux)	Yes — step up/down by transformer

Frequency f = 50 Hz ⟹ period T = 1/50 s for a full cycle, but a direction reversal happens every half-cycle = 1/100 s.

Practice this conceptself-check · 3 quick reps

Try it yourself

If a country's mains runs at 60 Hz, how often does the current reverse direction?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Indian mains frequency?
2.
How often does 50 Hz AC reverse direction?
3.
Which can a transformer change — AC or DC?

From the bank · past-year question

Example 5Electricity and MagnetismMODERATE

The AC mains domestic supply current in India changes direction in every

[Q122 · Sep · 2024]

Reverses every 1/100 s, not 1/50 s

The period of 50 Hz AC is 1/50 s — but that is one FULL cycle, which contains TWO reversals. The current changes direction every half-period = 1/100 s. Picking 1/50 s is the dominant trap.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Electric current as rate of flow of charge
Current and charge
$I = \dfrac{Q}{t} \quad\Longleftrightarrow\quad Q = I\,t$
Ohm's law — V = IR
Ohm's law
$V = I\,R$

Reference tables (1)

Alternating current vs direct current4 rows

Property	DC	AC
Direction	Constant (one way)	Reverses periodically
Source	Cell / battery / DC generator	AC generator / mains
Indian mains frequency	—	50 Hz (reverses every 1/100 s)Q NDA 2024 Sep — mains changes direction every 1/100 s, NOT 1/50 s: a 50 Hz cycle reverses TWICE per cycle.
Transformable?	No (transformers need changing flux)	Yes — step up/down by transformer

Frequency f = 50 Hz ⟹ period T = 1/50 s for a full cycle, but a direction reversal happens every half-cycle = 1/100 s.

Watch out for (5)

Convert minutes to seconds first
→ Electric current as rate of flow of charge
Free electrons, not 'both bound and free'
→ What carries current in a metal — free electrons
Ohm's law is NOT universal
→ Ohm's law — V = IR
A rheostat is ohmic; a diode is not
→ Ohmic vs non-ohmic conductors
Reverses every 1/100 s, not 1/50 s
→ Alternating current vs direct current

Mastery check — 4 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Electricity and MagnetismHARD

If the current through an electrical machine running on direct current is 15 A and the machine runs for 10 minutes, the charge that passes through the machine during this time is :

[Q53 · Apr · 2024]

Example 2Electricity and MagnetismMODERATE

Which one of the following statements regarding Ohm's law is not correct?

[Q54 · Sep · 2019]

Example 3Electricity and MagnetismEASY

A current of 1·0 A is drawn by a filament of an electric bulb for 10 minutes. The amount of electric charge that flows through the circuit is

[Q77 · Apr · 2021]

Example 4Electricity and MagnetismHARD

The graphs between current (

I

) and voltage (

V

) for three linear resistors 1, 2 and 3 are given. If

R_1

R_2

and

R_3

are the resistances of these resistors, then which one of the following is correct?

[Q93 · Sep · 2018]

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