Current Electricity Formula Sheet — JEE Main Physics

Q: What are the most important Current Electricity formulas for JEE Main?

This Current Electricity formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Electric current, Flow of electric charges in a metallic conductor, Drift velocity, Mobility and their relation with electric current, Ohm's law — each shown with the key result and, where useful, a worked example.

Q: Is this Current Electricity formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

Q: How should I revise Current Electricity formulas?

Blurt the Current Electricity formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Every key Current Electricity formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 21 sub-topics

Electric current
Flow of electric charges in a metallic conductor
Drift velocity
Mobility and their relation with electric current
Ohm's law
Electrical resistance
V-I characteristics (linear and non-linear)
Electrical energy and power
Electrical resistivity and conductivity
Carbon resistors
Colour code for carbon resistors
Series and parallel combinations of resistors
Temperature dependence of resistance
Internal resistance of a cell
Potential difference and emf of a cell
Combination of cells in series and in parallel
Kirchhoff's laws and simple applications
Wheatstone bridge
Metre bridge
Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells
Measurement of internal resistance of a cell

Electric Current & Drift Velocity

Electric current

I = \frac{q}{t} = \frac{d q}{d t}

conventional current is

opposite

to electron flow; unit ampere (A)

Drift velocity & current

v_{d} = \frac{e E τ}{m}; I = neAv_{d}

τ =

relaxation time,

n =

free-electron density,

A =

area,

e =

electron charge

Electrons in a conductor drift opposite to the applied field E with drift velocity v_d producing current I=neAv_d — Electrons drift opposite to $E$ .

Comparative: the three transport quantities

Quantity	Formula	Meaning
Drift velocity $v_{d}$	$e E τ / m$	mean electron speed
Current density $J$	$I / A = n e v_{d} = σ E$	current per area
Mobility $μ$	$v_{d} / E = e τ / m$	drift speed per field

🚫 Examiner Trap · Current & drift

(1) Conventional current is

opposite

to electron motion. (2) Drift speed is tiny (

\sim

mm/s) yet the bulb lights instantly — the field propagates at

\sim c

, not the electrons. (3)

v_{d} \propto E \propto V

, so current

\propto V

(Ohm). (4) Current is a

scalar

but

J

is a vector.

Ohm's Law, Resistance & Resistivity

Ohm's law

V = I R; J = σ E (microscopic)

R =

resistance,

σ =

conductivity; holds for

ohmic

conductors at fixed T

Resistance & resistivity

R = \frac{ρl}{A}; ρ = \frac{m}{n e ^{2} τ} = \frac{1}{σ}

ρ =

resistivity (material + T only, NOT shape);

l =

length,

A =

area

V-I graph: straight line for an ohmic conductor and a curve for a non-ohmic device — Ohmic $=$ linear; non-ohmic (diode, GaAs) $=$ curved.

Temperature dependence

ρ_{T} = ρ_{0} [1 + α (T - T_{0})]; R_{T} = R_{0} [1 + α Δ T]

α =

temperature coefficient of resistivity (

K^{- 1}

)

Comparative:

ρ

vs temperature

Material	$α$	$ρ$ as $T ↑$
Metal	$> 0$	rises
Semiconductor / insulator	$< 0$	falls ( $n ↑$ )
Alloy (manganin)	$\approx 0$	nearly constant
Superconductor	—	$0$ below $T_{c}$

🚫 Examiner Trap · Ohm, resistance & resistivity

(1)

ρ

depends on material & T

only

— stretching a wire changes R (via l,A) but not

ρ

. (2) Stretch to

n \times

length (volume fixed)

\Rightarrow R \to n^{2} R

. (3) Metals:

ρ ↑

with T (

τ ↓

); semiconductors:

ρ ↓

(

n ↑

). (4) Ohm's law is

not

universal — diodes/GaAs are non-ohmic.

Combination of Resistors

Comparative: series vs parallel

	Series	Parallel
Effective $R$	$\sum R_{i}$	$\frac{1}{R} = \sum \frac{1}{R _{i}}$
Same for all	current $I$	voltage $V$
Divides	$V \propto R$	$I \propto 1/ R$
$R_{e ff}$ vs members	$>$ largest	$<$ smallest

Series / Parallel

R_{s} = R_{1} + R_{2} + \dots; \frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

two in parallel:

R = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

Three resistors in series and three in parallel with their equivalent-resistance formulas — Series (same $I$ ) vs parallel (same $V$ ).

Useful results

▸n equal resistors R: series nR, parallel $R / n$ (ratio $n^{2}$ ).
▸Stretching a wire to $n \times$ length: $R \to n^{2} R$ (volume constant).
▸Balanced Wheatstone arm carries no current $\Rightarrow$ remove it when reducing.

🚫 Examiner Trap · Resistor combinations

(1) Parallel R is

less

than the smallest member — opposite to series. (2) Identify nodes first; resistors between the SAME two nodes are in parallel even if drawn far apart. (3) In a balanced bridge the central arm has

I = 0

— short/remove it to simplify. (4) Symmetry (Wheatstone, cube of resistors) collapses many networks fast.

Cells: EMF, Internal Resistance & Grouping

EMF

ε

: Work done per unit charge by the cell; equals the terminal voltage on

open

circuit (

I = 0

). Internal resistance r models energy lost inside.

Terminal voltage

V = ε - I r (discharge); I = \frac{ε}{R + r}

charging:

V = ε + I r

; short circuit

I_{ma x} = ε / r

;

V < ε

under load

A cell of emf and internal resistance r driving an external resistor R, with terminal voltage V=epsilon-Ir — Internal resistance drops the terminal voltage.

Comparative: grouping

n

identical cells

Grouping	Current $I$	Best when
Series	$\frac{n ε}{R + n r}$	$R ≫ r$
Parallel	$\frac{ε}{R + r / n}$	$R ≪ r$
Mixed ( $m$ rows)	$\frac{nm ε}{m R + n r}$	$R = n r / m$

🚫 Examiner Trap · Cells & grouping

(1) Terminal

V = ε - I r

on discharge but

ε + I r

while

charging

— sign flips. (2)

V = ε

only at

I = 0

(open circuit); under load

V < ε

. (3) Mixed grouping gives max current when external

R =

total internal

n r / m

. (4) Identical cells in parallel: emf stays

ε

, internal resistance becomes

r / n

Kirchhoff's Laws & Electrical Power

Kirchhoff's laws

KCL: \sum I = 0 (junction); KVL: \sum I R = \sum ε (loop)

KCL

=

charge conservation; KVL

=

energy conservation

Junction rule with currents in and out, and a loop with a resistor and a cell — Junction (KCL) and loop (KVL) rules.

Power & energy

P = V I = I^{2} R = \frac{V ^{2}}{R}; H = I^{2} Rt

Joule heating;

1 kWh = 3.6 \times 1 0^{6}

J (commercial unit)

Maximum power transfer

P_{ma x} = \frac{ε ^{2}}{4 r} when R = r

efficiency only

50%

at max power

Comparative: bulbs (rated

P

V

)

	Series	Parallel
Combined $P$	$\frac{1}{P} = \sum \frac{1}{P _{i}}$	$P = \sum P_{i}$
Brighter bulb	$lower$ -watt	higher-watt
Reason	same I, $P = I^{2} R$	same V, $P = V^{2} / R$

🚫 Examiner Trap · Kirchhoff & power

(1) A bulb's resistance

R = V^{2} / P_{r a t e d}

— use

rated

values to get R, then recompute P in the actual circuit. (2) In

series

, the lower-wattage (higher-R) bulb glows

brighter

— counter-intuitive. (3) Max-power (

R = r

) wastes half the energy in r. (4) Transmit at high V: line loss

P_{c} = P^{2} R_{c} / V^{2}

Wheatstone & Metre Bridge

Wheatstone balance

\frac{P}{Q} = \frac{R}{S} (galvanometer I_{G} = 0)

P, Q, R, S =

the four arm resistances

Wheatstone bridge: four resistors P, Q, R, S in a diamond with a galvanometer across one diagonal and a cell across the other — Balanced when no current flows through G.

Metre bridge

\frac{R}{S} = \frac{l}{100 - l} \Rightarrow S = R \frac{100 - l}{l}

l =

balancing length (cm) from the left end

Why it is accurate

▸A $null$ method — reading is independent of cell EMF and galvanometer calibration.
▸Most sensitive when the four arms are comparable (balance near the middle).
▸Interchanging battery and galvanometer does $not$ change the balance.

🚫 Examiner Trap · Bridges

(1) Balance condition is

P / Q = R / S

— at balance

I_{G} = 0

, so

galvanometer resistance is irrelevant

. (2) Metre-bridge: keep the balance point near the centre to minimise % error from end corrections. (3) Don't take readings with current flowing for long (heats the wire, shifts

ρ

). (4) The bridge measures a

ratio

, so a precise standard R is essential.

Potentiometer & Measuring Instruments

Potentiometer: Measures p.d. / EMF drawing

no current at balance

\Rightarrow

acts as an ideal voltmeter. Potential gradient

K = V / L

is constant on a uniform wire.

Uses

ε = K l; \frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}; r = R (\frac{l _{1} - l _{2}}{l _{2}})

l =

balance length; compare EMFs and find internal resistance

r

Potentiometer: driver cell and rheostat across a uniform wire, with a jockey and galvanometer locating the balance length for an unknown cell — Balance length l sets $ε = K l$ .

Comparative: ammeter vs voltmeter

	Ammeter	Voltmeter
Measures	current	p.d.
Connection	series	parallel
Resistance	low ( $0$ ideal)	high ( $\infty$ ideal)
Made from G by	shunt $S$ (parallel)	series $R$ (high)

Galvanometer conversion

shunt S = \frac{G i _{g}}{I - i _{g}}; series R = \frac{V}{i _{g}} - G

G =

galvo resistance,

i_{g} =

full-scale current

🚫 Examiner Trap · Potentiometer & meters

(1) A potentiometer beats a voltmeter because it draws

zero

current at balance (true EMF, not terminal V). (2) Ammeter in

series

(low R), voltmeter in

parallel

(high R) — swapping them can short the circuit. (3) To measure EMF the driver cell's emf must exceed the cell tested, else

no balance point

. (4) Longer wire

\Rightarrow

smaller K

\Rightarrow

higher sensitivity.

More JEE Main Physics formula sheets

Frequently Asked Questions

What are the most important Current Electricity formulas for JEE Main?

This Current Electricity formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Electric current, Flow of electric charges in a metallic conductor, Drift velocity, Mobility and their relation with electric current, Ohm's law — each shown with the key result and, where useful, a worked example.

Is this Current Electricity formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

How should I revise Current Electricity formulas?

Blurt the Current Electricity formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Also useful: all formula sheets · JEE Main previous-year papers · most important chapters.