KCET · Physics · Class XII / Second PUC · Unit II: Current Electricity

Electric Current, Drift Velocity and Ohm's Law

Inside every current-carrying wire, billions of free electrons drift slowly toward the positive terminal, buffeted constantly by collisions with the metal's ions. This lesson connects that microscopic picture — drift velocity — to the macroscopic current you measure with an ammeter, and introduces Ohm's Law, the single most-used relationship in circuit problems.

Live

Drift Velocity and Ohm's Law Circuit Lab

Switch between a microscopic Drift Velocity view (adjust carrier density and wire area to see individual charge carriers drift through a wire) and an Ohm's Law view (adjust resistance and voltage to see the V-I graph and verify the straight-line relationship).

Open Simulation

How to Use This Chapter

Read each band top to bottom, then try the linked Guided Practice questions before moving to the next band.

Electric Current as Rate of Charge Flow

Current: I = Q/t

Electric current is defined as the rate of flow of charge: I = Q/t (for steady current) or I = dQ/dt (for current that varies with time).

Principle

Current measures how much charge crosses a given cross-section of the conductor per unit time — a bulk, macroscopic quantity, unlike the microscopic drift velocity of individual carriers.

Example: A charge of 42 C flows through a wire in 6 s: I=Q/t=42/6=7 A.

KCET note: For a time-varying current, KCET may ask for total charge instead, using Q=∫I dt — the reverse of this formula.

Trap: Using I=dQ/dt as if it always equals Q/t — the dQ/dt form is only needed when current itself changes with time; for steady current, Q/t is sufficient.

Conventional Current vs Electron Drift Direction

By convention, current is taken to flow in the direction that POSITIVE charge would move — which is opposite to the actual direction free electrons drift in a metal.

Principle

This convention predates the discovery of the electron; it was kept because switching it now would be more confusing than useful, so all circuit diagrams and formulas use the 'positive charge flow' direction.

Example: In a wire connected so electrons drift from left to right, the conventional current is drawn flowing from right to left.

KCET note: This distinction rarely changes a numeric answer, but frequently appears in conceptual/direction-based questions.

Trap: Assuming conventional current and electron drift point the same way — in a metal, they are always opposite.

Drift Velocity and the Microscopic Picture

Drift Velocity: I = nAv_d e

Current relates to drift velocity by I = nAv_d e, where n is the number of free charge carriers per unit volume, A is the conductor's cross-sectional area, and e is the charge of an electron.

Principle

This connects the macroscopic, measurable current to the microscopic net velocity of the charge carriers — rearranged, v_d=I/(nAe).

Example: A wire with n=4×10²⁸ per m³, A=3×10⁻⁶ m², carrying I=2.4 A: v_d=2.4/(4×10²⁸×3×10⁻⁶×1.6×10⁻¹⁹)=2.4/(1.92×10⁴)=1.25×10⁻⁴ m/s.

KCET note: Always convert n and A to SI base units (per m³, m²) before substituting — mixing in cm³ or cm² is a common source of factor-of-10⁶ errors.

Trap: Forgetting one of the three factors (n, A, or e) in the denominator when solving for v_d.

Drift Velocity Is Tiny Compared to Thermal Speed

Free electrons in a conductor don't move in a straight line toward the positive terminal; they undergo constant random collisions with fixed ions, with only a slow net 'drift' superimposed on that chaos. Drift velocity v_d is typically a fraction of a millimetre per second — remarkably slow compared to how quickly a bulb lights up (that signal travels near light speed, not at the drift velocity).

Principle

Even with zero applied field, electrons already move at thermal speeds around 10⁵ m/s, in random directions averaging to zero net current. An applied field adds only a tiny net bias (~10⁻⁴ m/s) on top of this chaotic motion.

Example: A typical copper wire has thermal electron speeds around 10⁵ m/s but a drift velocity of only about 10⁻⁴ m/s — the drift is roughly a billion times slower than the underlying thermal motion.

KCET note: The near-instant response of a switched-on bulb is due to the electric field propagating at near light speed, not the electrons themselves travelling fast.

Trap: Believing current requires electrons to move fast along the wire — it's the field's rapid propagation, not fast electron travel, that makes circuits respond quickly.

Current Density and Non-Uniform Wires

Current Density: J = I/A = nev_d

Current density J = I/A is current per unit cross-sectional area, and equals nev_d — useful for comparing current flow across conductors of different thickness.

Principle

Unlike current I (which is conserved along a single wire), current density depends on the local cross-sectional area, so it varies from point to point in a non-uniform wire.

Example: A wire of area 3×10⁻⁶ m² carries 9 A: J=I/A=9/(3×10⁻⁶)=3×10⁶ A/m².

KCET note: J is a useful bridge quantity — if you know J and n, you can find v_d directly via v_d=J/(ne), without recomputing from I and A separately.

Trap: Treating current density as constant along a wire whose cross-section varies — J changes with A even though I itself doesn't.

Current Stays Constant; Drift Velocity and J Don't

In a single wire (no branching) with non-uniform cross-section, charge conservation means the current I is the SAME at every cross-section, thick or thin. Since I=nAv_d e and A changes, v_d (and hence J) must change inversely with A to keep I constant.

Principle

This is directly analogous to fluid flow through a pipe of varying width — the volume flow rate stays constant, so the fluid speeds up in narrower sections.

Example: The same current flows through a wide section (A=8×10⁻⁶ m²) and a narrow section (A=4×10⁻⁶ m²) of one wire. Since v_d∝1/A, the ratio v_d(narrow)/v_d(wide)=8/4=2 — drift velocity doubles in the narrower section.

KCET note: For ratio questions like this, n and e cancel out entirely — only the area ratio matters.

Trap: Assuming drift velocity or current density stays the same throughout a non-uniform wire — only the current I itself is guaranteed constant.

Ohm's Law and Ohmic Conductors

Ohm's Law: V = IR

Ohm's Law states that for a conductor at constant temperature, the current through it is directly proportional to the voltage across it: V = IR, where R is the resistance (a constant for that conductor at that temperature).

Principle

R itself is defined as the constant of proportionality V/I, and for an ohmic conductor, this ratio stays fixed regardless of how much voltage or current is applied.

Example: A resistor of 6 Ω carries 3.5 A: V=IR=6×3.5=21 V.

KCET note: Ohm's Law questions can ask for any one of V, I, or R given the other two — rearrange the formula as needed.

Trap: Applying V=IR to a device whose resistance changes with current or temperature (like a bulb filament at high current) — Ohm's Law assumes R stays constant.

Ohmic vs Non-Ohmic Conductors

Materials that obey Ohm's Law (V directly proportional to I) are called ohmic conductors; materials like diodes and semiconductor junctions do NOT obey a simple proportional V-I relationship and are called non-ohmic. For an ohmic conductor, a graph of V versus I is a straight line through the origin, and its slope gives R.

Principle

A curved or non-origin-passing V-I graph signals non-ohmic behaviour — the 'resistance' at different points on such a curve isn't a single fixed value.

Example: A metal wire at constant, moderate temperature gives a straight-line V-I graph through the origin (ohmic); a semiconductor diode gives a sharply curved graph that isn't even symmetric for positive and negative voltage (non-ohmic).

KCET note: KCET frequently tests this distinction conceptually — recognizing which named devices are ohmic (resistors, metal wires at constant T) versus non-ohmic (diodes, transistors, bulb filaments at high current).

Trap: Assuming every conductor obeys Ohm's Law just because V=IR can always be used to DEFINE a resistance at one operating point — the LAW requires that ratio to stay constant across different V and I values.

Applying Ohm's Law and the Ampere

Verifying Ohm's Law from Experimental Data

Given two or more (V, I) data pairs for a conductor, Ohm's Law holds if and only if V/I comes out the SAME for every pair — that common ratio is the resistance R.

Principle

This is exactly how Ohm's Law is verified experimentally: plot V against I, and check whether the points fall on a single straight line through the origin.

Example: A conductor draws 2 A at 14 V, and 3 A at 21 V. R₁=14/2=7 Ω, R₂=21/3=7 Ω — since both ratios match, the conductor is ohmic with R=7 Ω.

KCET note: If the ratios DON'T match across different data pairs, the conductor is non-ohmic, and no single 'resistance' value describes it.

Trap: Computing only one V/I ratio and assuming Ohm's Law holds — you must check that the ratio stays the same across at least two different operating points.

The Ampere: SI Unit of Current

The SI unit of current is the ampere (A), defined as one coulomb of charge flowing per second (1 A = 1 C/s).

Principle

This definition follows directly from I=Q/t: an ampere is simply the specific rate of charge flow that corresponds to 1 coulomb every 1 second.

Example: If 5 C of charge flows past a point in exactly 1 s, the current is exactly 5 A, by the ampere's own definition.

KCET note: Don't confuse the ampere (a rate of charge flow) with the coulomb (a quantity of charge) — they measure different things, related by I=Q/t.

Trap: Confusing the ampere with a unit of charge rather than a unit of RATE of charge flow.

Learning Outcomes

Apply I=Q/t to relate current, charge, and time.
Compute drift velocity from current, carrier density, and cross-sectional area, and explain why it is so much smaller than the electrons' thermal speed.
Compute current density, and explain why current (not current density or drift velocity) stays constant along a single non-uniform wire.
Apply Ohm's Law (V=IR) and distinguish ohmic from non-ohmic conductors using their V-I graphs.
Verify whether a conductor is ohmic from experimental (V,I) data pairs, and state the definition of the ampere.

Common Misconceptions

Conventional Current Confused with Electron Flow: Assuming conventional current flows the same direction as electron drift — in a metal, they are always opposite.
Drift Velocity Assumed to Be Fast: Believing electrons move quickly along the wire — drift velocity is only a fraction of a mm/s; it's the field that propagates fast.
Current Density Assumed Constant in a Non-Uniform Wire: Treating J (or v_d) as constant along a wire of varying cross-section — only the current I itself is guaranteed constant.
Ohm's Law Applied to Non-Ohmic Devices: Using V=IR with a fixed R for devices like diodes or high-current bulb filaments, where resistance isn't actually constant.
Ampere Confused with a Unit of Charge: Treating the ampere as a quantity of charge rather than a RATE of charge flow (C/s).

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