Physics · Electromagnetism

Current Electricity formulas for JEE

Every Current Electricity formula you need for JEE, grouped by concept.

FormulasRevision notes
54 formulas3 concepts
01Electric Current and Ohm's Law02Circuits and Resistors03Kirchhoff's Laws and Devices
01

Electric Current and Ohm's Law

20 formulas

Conductivity Formula

σ=ne2τm\sigma = \frac{ne^2\tau}{m}

Conductivity in terms of charge carrier properties.

conductivityrelaxation_timedensity

Drift Velocity

vd=−eEτm\mathbf{v}_d = -\frac{e\mathbf{E}\tau}{m}

Average steady velocity of charge carriers under an applied electric field.

applies whenSteady state, constant relaxation time.
drift_velocityrelaxation_timevector

Electron Acceleration

a=−eEm\mathbf{a} = -\frac{e\mathbf{E}}{m}

Acceleration of a free electron in an electric field between collisions.

applies whenBetween successive collisions with ions.
electronaccelerationkinematics

Average Electric Current

I=ΔQΔtI = \frac{\Delta Q}{\Delta t}

Definition of average electric current over a time interval.

applies whenSteady or average flow of charge.
currentcharge

Current from Drift Velocity

I=neA∣vd∣I = neA|v_d|

Macroscopic current related to microscopic drift velocity.

applies whenUniform cross-section.
currentdrift_velocitymicroscopic

Instantaneous Electric Current

I=lim⁡Δt→0ΔQΔt=dQdtI = \lim_{\Delta t \to 0} \frac{\Delta Q}{\Delta t} = \frac{dQ}{dt}

Current at a specific instant as the time interval approaches zero.

currentchargeinstantaneous

Current from Current Density

I=∬j⋅dSI = \iint \mathbf{j} \cdot d\mathbf{S}

Current defined as the surface integral of current density.

applies whenNon-uniform current density.
currentcurrent_densityvectorjee-advanced

Current Density Magnitude

j=IAj = \frac{I}{A}

Current per unit area perpendicular to the flow.

applies whenUniform current distribution over the area.
current_densityarea

Current Density from Drift

j=−nevd\mathbf{j} = -ne\mathbf{v}_d

Vector relationship between current density and drift velocity.

applies whenFor electrons (negative charge).
current_densitydrift_velocityvector

Carrier Mobility

μ=∣vd∣E\mu = \frac{|v_d|}{E}

Mobility defined as drift velocity magnitude per unit electric field.

mobilitydrift_velocity

Mobility and Relaxation Time

μ=eτm\mu = \frac{e\tau}{m}

Mobility expressed in terms of charge, mass, and relaxation time.

mobilityrelaxation_time

Ohm's Law

V=IRV = IR

Macroscopic relationship between voltage, current, and resistance.

applies whenValid for ohmic conductors at constant temperature.
ohm's_lawvoltageresistance

Microscopic Ohm's Law

j=σE\mathbf{j} = \sigma \mathbf{E}

Vector relationship between current density, conductivity, and electric field.

applies whenIsotropic ohmic materials.
ohm's_lawmicroscopicconductivityvector

Electrical Power (I²R)

P=I2RP = I^2 R

Ohmic power loss in a resistor.

applies whenOhmic conductor.
powerohmic_loss

Electrical Power (V²/R)

P=V2RP = \frac{V^2}{R}

Ohmic power in terms of voltage and resistance.

applies whenOhmic conductor.
powervoltage

Electrical Power (VI)

P=IVP = IV

Power supplied or dissipated in a component.

powervoltagecurrent

Resistance from Resistivity

R=ρlAR = \rho \frac{l}{A}

Resistance of a uniform conductor in terms of its dimensions and resistivity.

applies whenUniform cross-section and homogeneous material.
resistanceresistivitygeometry

Temperature Dependence of Resistance

RT=R0[1+α(T−T0)]R_T = R_0 [1 + \alpha(T - T_0)]

Linear approximation for resistance at temperature T.

applies whenValid over a limited temperature range for metals.
temperatureresistance

Average Thermal Velocity

1N∑vi=0\frac{1}{N} \sum \mathbf{v}_i = 0

The vector sum of thermal velocities of all electrons in a conductor is zero.

applies whenMacroscopic scale, in the absence of an applied electric field.
thermal_velocityaverage

RMS Thermal Speed

vrms=3kBTmv_{rms} = \sqrt{\frac{3k_B T}{m}}

Thermal speed of charge carriers/atoms based on kinetic theory.

applies whenIdeal gas approximation.
thermal_speedtemperature
02

Circuits and Resistors

25 formulas

Cell Current

I=ϵR+rI = \frac{\epsilon}{R+r}

Current drawn from a cell connected to an external resistor.

applies whenSimple single-loop circuit.
currentcell_circuit

Resistance of Cylindrical Shell

R=ρ2πLln⁡(ba)R = \frac{\rho}{2\pi L} \ln\left(\frac{b}{a}\right)

Resistance of a cylindrical shell of length L, inner radius a, outer radius b.

applies whenCurrent flows radially outward.
resistancegeometrycalculusjee-advanced

Electrical Work

ΔW=IVΔt\Delta W = I V \Delta t

Energy dissipated as heat by a current passing through a potential difference.

applies whenConstant current and voltage over time.
workenergyheat

Electromotive Force (EMF)

ϵ=V++V−\epsilon = V_+ + V_-

Potential difference of a cell in an open circuit.

applies whenOpen circuit (no current flowing).
emfcell

Infinite Ladder Equivalent Resistance

Req=R1+R2ReqR2+ReqR_{eq} = R_1 + \frac{R_2 R_{eq}}{R_2 + R_{eq}}

Standard infinite ladder condition.

applies whenRepeating L-section. Must reject negative roots.
infinite_laddercircuitsjee-advanced

Maximum Power Transfer

Pmax=ϵ24rP_{max} = \frac{\epsilon^2}{4r}

Maximum power delivered to an external load.

applies whenExternal resistance equals internal resistance (R = r).
powermaximum_powerjee-advanced

Mixed Grouping of Cells

I=mnϵmR+nrI = \frac{mn\epsilon}{mR + nr}

Current from an m-row, n-column grid of cells.

applies whenm parallel rows, n cells in series per row.
mixed_groupingcellsjee-advanced

Resistors in Parallel

1Req=∑i1Ri\frac{1}{R_{eq}} = \sum_{i} \frac{1}{R_i}

Equivalent resistance for resistors in parallel.

parallelresistors

Parallel Cells Equivalent EMF

ϵeqreq=∑iϵiri\frac{\epsilon_{eq}}{r_{eq}} = \sum_{i} \frac{\epsilon_i}{r_i}

Equivalent EMF for a parallel combination of cells.

applies whenPositive terminals connected together.
parallelemfcells

Parallel Cells Internal Resistance

1req=∑i1ri\frac{1}{r_{eq}} = \sum_{i} \frac{1}{r_i}

Equivalent internal resistance for a parallel combination of cells.

parallelinternal_resistance

Electrical Power (I²R)

P=I2RP = I^2 R

Ohmic power loss in a resistor.

applies whenOhmic conductor.
powerohmic_loss

Transmission Power Loss

Pc=P2RcV2P_c = \frac{P^2 R_c}{V^2}

Power wasted as heat in transmission lines.

applies whenP is the transmitted power, V is the transmission voltage.
powertransmission_loss

Electrical Power (V²/R)

P=V2RP = \frac{V^2}{R}

Ohmic power in terms of voltage and resistance.

applies whenOhmic conductor.
powervoltage

Electrical Power (VI)

P=IVP = IV

Power supplied or dissipated in a component.

powervoltagecurrent

Resistors in Series

Req=∑iRiR_{eq} = \sum_{i} R_i

Equivalent resistance for resistors in series.

seriesresistors

Series Cells Equivalent EMF

ϵeq=∑iϵi\epsilon_{eq} = \sum_{i} \epsilon_i

Equivalent EMF of cells connected in series assisting each other.

applies whenCells connected with matching polarities.
seriesemfcells

Series Cells Internal Resistance

req=∑irir_{eq} = \sum_{i} r_i

Equivalent internal resistance of cells in series.

seriesinternal_resistance

Resistance of Spherical Shell

R=ρ4π(1a−1b)R = \frac{\rho}{4\pi}\left(\frac{1}{a} - \frac{1}{b}\right)

Resistance of a spherical shell between inner radius a and outer radius b.

applies whenCurrent flows radially outward.
resistancegeometrycalculusjee-advanced

Star-Delta Transformation

R1=RbRcRa+Rb+RcR_1 = \frac{R_b R_c}{R_a + R_b + R_c}

Equivalent star branch resistance from delta resistors.

applies whenDelta-Star simplification.
star_deltacircuitsjee-advanced

Temperature Dependence of Resistance

RT=R0[1+α(T−T0)]R_T = R_0 [1 + \alpha(T - T_0)]

Linear approximation for resistance at temperature T.

applies whenValid over a limited temperature range for metals.
temperatureresistance

Platinum Resistance Thermometer

t=Rt−R0R100−R0×100t = \frac{R_t - R_0}{R_{100} - R_0} \times 100

Interpolation formula to find temperature from resistance.

applies whenLinear resistance assumption.
temperaturethermometer

Temperature Dependence of Resistivity

ρT=ρ0[1+α(T−T0)]\rho_T = \rho_0 [1 + \alpha(T - T_0)]

Linear approximation for resistivity at temperature T.

applies whenValid over a limited temperature range.
temperatureresistivity

Terminal Voltage (Discharging)

V=ϵ−IrV = \epsilon - Ir

Terminal voltage across a cell providing current.

applies whenCell is discharging.
terminal_voltagedischarging

Terminal Voltage (Charging)

V=ϵ+IrV = \epsilon + Ir

Terminal voltage across a cell being charged.

applies whenCell is being charged by an external source.
terminal_voltagechargingjee-advanced

Resistance of Truncated Cone

R=ρLπabR = \frac{\rho L}{\pi a b}

Resistance of a solid truncated cone of radii a and b, length L.

applies whenCurrent flows longitudinally.
resistancegeometrycalculusjee-advanced
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03

Kirchhoff's Laws and Devices

9 formulas

Kirchhoff's Junction Rule (KCL)

∑Iin=∑Iout\sum I_{in} = \sum I_{out}

Sum of currents entering a junction equals sum of currents leaving.

applies whenBased on conservation of charge.
kirchhoffjunction

Kirchhoff's Loop Rule (KVL)

∑ΔV=0\sum \Delta V = 0

Algebraic sum of changes in potential around any closed loop is zero.

applies whenBased on conservation of energy.
kirchhoffloop

Meter Bridge Balance

R=Sl100−lR = S \frac{l}{100 - l}

Formula to determine unknown resistance in a meter bridge.

applies whenAssuming a 100 cm uniform wire.
meter_bridgeinstrument

Comparing EMFs via Potentiometer

ϵ1ϵ2=l1l2\frac{\epsilon_1}{\epsilon_2} = \frac{l_1}{l_2}

Ratio of EMFs equals ratio of balancing lengths.

applies whenNull deflection.
potentiometeremfinstrumentjee-advanced

Internal Resistance via Potentiometer

r=R(l1l2−1)r = R\left(\frac{l_1}{l_2} - 1\right)

Finding internal resistance using open and shunted balancing lengths.

applies whenNull deflection.
potentiometerinternal_resistanceinstrumentjee-advanced

Wheatstone Bridge Balance

R2R1=R4R3\frac{R_2}{R_1} = \frac{R_4}{R_3}

Condition for null deflection in the galvanometer.

applies whenCurrent through galvanometer is zero.
wheatstone_bridgebalance

Ammeter Shunt Resistance

rs=IgRGI−Igr_s = \frac{I_g R_G}{I - I_g}

Shunt resistance required to convert a galvanometer into an ammeter.

applies whenDesired range I, galvanometer full scale current I_g.
ammeterconversionjee-advanced

Galvanometer Current Sensitivity

Is=θI=NABkI_s = \frac{\theta}{I} = \frac{NAB}{k}

Deflection per unit current in a moving coil galvanometer.

applies whenRadial magnetic field.
galvanometersensitivityjee-advanced

Voltmeter Series Resistance

R=VIg−GR = \frac{V}{I_g} - G

Series resistance to convert galvanometer to a voltmeter.

galvanometervoltmeterinstrumentjee-advanced
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