Current Electricity Short Notes for JEE Main: Revision Notes PDF

Current, drift velocity and resistance

Electric current

4× asked, last 2024

I=\frac{dq}{dt},\qquad q=\int I\,dt,\qquad \frac{dN}{dt}=\frac{I}{e}

q

= area under the

I

–

t

graph. Electrons crossing per second

=I/e

. 1 A = 1 C s⁻¹.

t

(s)

I

(A)O426

q=16

q

= area

=\tfrac12(2+6)\times4=16

C, not

6\times4

Not $q=It$ with the final current. When $I$ changes with time, integrate between the two times (or take the area under the $I$ – $t$ graph). For linear $I$ , $q$ = average current × time.

Drift velocity and mobility

8× asked, last 2026

I=neAv_d,\qquad v_d=\frac{eE\tau}{m}=\frac{eV\tau}{mL},\qquad \mu=\frac{v_d}{E}=\frac{e\tau}{m}

n

= free electrons per m³,

\tau

= relaxation time. 1 mm²

=10^{-6}

m².

\mu

in m² V⁻¹ s⁻¹.

\vec E

startnet drift

v_d

An electron between collisions: paths curve under

e\vec E/m

, so it creeps against

\vec E

Fixed $V$ across a wire: $v_d\propto1/L$ and does not depend on $A$ . Fixed $I$ (one series path): $v_d\propto1/A$ , so electrons drift faster where the wire is thinner.
At fixed $V$ , heating shortens $\tau$ , so $v_d$ falls (at fixed $I$ , $v_d=I/(neA)$ is unchanged). Electrons drift against $\vec E$ , from lower to higher potential, on curved paths between collisions; $v_d$ is only about mm/s.

Current density and conductivity

5× asked, last 2022

J=\frac{I}{A}=nev_d,\qquad \vec J=\sigma\vec E,\qquad \sigma=\frac1\rho=\frac{ne^2\tau}{m}=ne\mu

Uniform

J

through a ring of radii

r_1,r_2

I=J\pi(r_2^2-r_1^2)

. Force on each electron

=eE=e\rho J

Not $I=JA$ when $\vec J$ is tilted. $I=\vec J\cdot\vec A=JA\cos\theta$ , with $\theta$ measured from the normal to the area.

Resistance and resistivity

14× asked, last 2025

R=\frac{\rho L}{A},\qquad \rho=\frac{m}{ne^2\tau}

\rho

depends on material and temperature, not on shape. Order: Cu < Al < W < Hg.

Hollow tube: $A=\pi(r_2^2-r_1^2)$ . Current flowing radially between coaxial cylinders of radii $a<b$ and length $l$ : $R=\rho\ln(b/a)/2\pi l$ .
Fixed volume $V$ (same mass): $R=\rho L^2/V=\rho V/A^2$ , so $R\propto L^2\propto1/r^4$ . $N$ identical wires in parallel act as one wire with $N$ times the area.

Stretching a wire

11× asked, last 2024

L\to nL:\ R'=n^2R,\qquad r\to \frac rn:\ R'=n^4R,\qquad \frac{\Delta R}{R}\approx\frac{2\Delta L}{L}

Volume kept constant (stretched, drawn or melted). The

2\Delta L/L

rule holds only for a few per cent.

stretch %

\Delta R/R

(%)O1020204060

21\%

, not

20\%

exact

(1+x)^2-1

2x

Volume fixed: the

2\Delta L/L

rule drifts off as the stretch grows

Not twice the stretch for large changes. Use $(1+x)^2-1$ : a 10% stretch gives 21%, not 20%. If length and area are given separately (volume not kept), use $R\propto L/A$ directly.
Not $nL$ for 'increased by $n$ times'. NTA reads it as $(n+1)L$ , so $R'=(n+1)^2R$ . 'Increased to' or 'stretched to' $n$ times is $nL$ : rise $(n^2-1)\times100\%$ , not $n^2\times100\%$ .

Temperature dependence

12× asked, last 2026

R_T=R_0(1+\alpha\,\Delta T),\qquad \rho_T=\rho_0(1+\alpha\,\Delta T)

\alpha>0

for metals,

<0

for semiconductors. Manganin, constantan: tiny

\alpha

, high

\rho

: standard resistors.

T

(K)

\rho/\rho_{300}

3001metalalloysemiconductor

Metals:

\tau

falls, so

\rho

rises. Semiconductors:

n

rises faster, so

\rho

falls

Series: $\alpha=(R_1\alpha_1+R_2\alpha_2)/(R_1+R_2)$ , zero when $R_1\alpha_1=-R_2\alpha_2$ . Parallel: $\alpha\approx(R_2\alpha_1+R_1\alpha_2)/(R_1+R_2)$ . Equal $R_0$ : both give $(\alpha_1+\alpha_2)/2$ .
Why: $\rho=m/(ne^2\tau)$ . Metals: $\tau$ falls as $T$ rises, so $\rho$ rises. Semiconductors: $n$ rises much faster, so $\rho$ falls. Alloys like nichrome change very little.
Not $\Delta R/(R_1\Delta T)$ when the readings are far apart. $\alpha$ is defined from $R_0$ at 0 °C. Write $R_1=R_0(1+\alpha t_1)$ , $R_2=R_0(1+\alpha t_2)$ and divide. At fixed $V$ , use $R=V/I$ .

Ohm's law and the V–I experiment

4× asked, last 2024

V=IR,\qquad R=\text{slope of the }V\text{–}I\text{ graph}

Ohmic: straight line through the origin at fixed temperature. Non-ohmic: curved or one-way (lamp, diode); use

R=V/I

R

(wire)rheostatV

Ammeter in series with the wire, voltmeter across it, rheostat to vary

I

I

(A)

V

(V)O210

V

on y: slope

=R=5\,\Omega

V

(V)

I

(A)O102

I

on y: slope

=1/R

NTA experiment: ammeter in series with the wire, voltmeter in parallel across it, rheostat to vary $I$ . Plot $V$ against $I$ ; $R$ = slope.
Not the slope as $R$ on an $I$ – $V$ graph. With $I$ on the y-axis, $R=1/\text{slope}$ . Check the axes and the prefixes (mA, kΩ) before reading the slope.

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19 more concepts in 5 topics

Resistor combinations and networks; Kirchhoff's laws and meters; Cells, emf and internal resistance; Electrical power and heating; and Bridges, divider and potentiometer. Read the first part free. Sign in free with Google to read the rest and download the PDF.

Resistor combinations and networks

Series and parallel29×
Wire bent into a loop7×
Symmetric networks15×
Infinite ladder1×

Kirchhoff's laws and meters

Kirchhoff's laws36×
Ammeters and voltmeters11×
Capacitor in a DC circuit5×
Also remember1

Cells, emf and internal resistance

EMF and terminal voltage13×
Cells in series8×
Cells in parallel and mixed12×
Maximum power transfer2×

Electrical power and heating

Joule heating19×
Rated bulbs and devices8×
Heating time with two coils2×
Energy, kWh and transmission5×

Bridges, divider and potentiometer

Wheatstone bridge11×
Metre bridge (NTA experiment)13×
Potential divider and rheostat6×
Potentiometer (dropped 2024, still asked)20×

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Current Electricity revision notes

Current, drift velocity and resistance

19 more concepts in 5 topics

Resistor combinations and networks

Kirchhoff's laws and meters

Cells, emf and internal resistance

Electrical power and heating

Bridges, divider and potentiometer

Practise Current Electricity next

Also free on PrepWiser

Downloading Current Electricity revision notes (PDF)

Current Electricity revision notes

1Current, drift velocity and resistance7 concepts

19 more concepts in 5 topics

2Resistor combinations and networks4 concepts

3Kirchhoff's laws and meters3 concepts

4Cells, emf and internal resistance4 concepts

5Electrical power and heating4 concepts

6Bridges, divider and potentiometer4 concepts

Practise Current Electricity next

Also free on PrepWiser

Current, drift velocity and resistance

Resistor combinations and networks

Kirchhoff's laws and meters

Cells, emf and internal resistance

Electrical power and heating

Bridges, divider and potentiometer