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Current Electricity formulas

Master Current Electricity through 32 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Current Electricity, every formula

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Average current
$I_{a v} = \frac{Δ q}{Δ t}$
Instantaneous current
$I = \frac{d q}{d t}$
Q1MCQInstantaneous current
Instantaneous current is:
- A
  $\dfrac{dq}{dt}$
- B
  $\dfrac{\Delta q}{\Delta t}$
- C
  $qt$
- D
  $\dfrac{q}{t^{2}}$
Current from drift velocity
$I = n e A v_{d}$
Q1MCQDrift current
The current in terms of drift velocity is:
- A
  $neAv_d$
- B
  $\dfrac{neA}{v_d}$
- C
  $nev_d$
- D
  $eAv_d$
Drift velocity
$v_{d} = \frac{e E τ}{m}$
Q1MCQDrift velocity
The drift velocity of electrons is:
- A
  $\dfrac{eE\tau}{m}$
- B
  $\dfrac{eE}{m}$
- C
  $\dfrac{E\tau}{m}$
- D
  $eE\tau$
Mobility
$μ = \frac{v _{d}}{E} = \frac{e τ}{m}$
Q1MCQMobility
The mobility of a charge carrier is:
- A
  $\dfrac{v_d}{E}$
- B
  $v_d E$
- C
  $\dfrac{E}{v_d}$
- D
  $eE$
Current density
$J = \frac{I}{A} = σ E$
Q1MCQCurrent density
The current density is:
- A
  $\dfrac{I}{A}$
- B
  $IA$
- C
  $\dfrac{A}{I}$
- D
  $I^{2}A$
Resistance of a conductor
$R = \frac{ρl}{A}$
Q1MCQResistance
The resistance of a wire is:
- A
  $\dfrac{\rho l}{A}$
- B
  $\dfrac{\rho A}{l}$
- C
  $\rho l A$
- D
  $\dfrac{l}{\rho A}$
Resistivity
$ρ = \frac{m}{n e ^{2} τ} = \frac{1}{σ}$
Q1MCQResistivity
Resistivity in terms of relaxation time is:
- A
  $\dfrac{m}{ne^{2}\tau}$
- B
  $\dfrac{ne^{2}\tau}{m}$
- C
  $\dfrac{m\tau}{ne^{2}}$
- D
  $ne^{2}\tau$
Ohm's law
$V = I R$
Temperature dependence
$R = R_{0} (1 + α Δ T)$
Q1MCQTemperature
The resistance at temperature $T$ is:
- A
  $R_0(1+\alpha\Delta T)$
- B
  $R_0(1-\alpha\Delta T)$
- C
  $R_0\alpha\Delta T$
- D
  $R_0$
Series combination
$R_{e q} = R_{1} + R_{2} + \dots$
Parallel combination
$\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$
Voltage division (series)
$V_{1} = \frac{R _{1}}{R _{1} + R _{2}} V$
Q1MCQVoltage division
In series, the voltage across $R_1$ is:
- A
  $\dfrac{R_1}{R_1+R_2}V$
- B
  $\dfrac{R_2}{R_1+R_2}V$
- C
  $\dfrac{V}{R_1}$
- D
  $V$
Current division (parallel)
$I_{1} = \frac{R _{2}}{R _{1} + R _{2}} I$
Q1MCQCurrent division
In parallel, the current through $R_1$ is:
- A
  $\dfrac{R_2}{R_1+R_2}I$
- B
  $\dfrac{R_1}{R_1+R_2}I$
- C
  $\dfrac{I}{R_1}$
- D
  $I$
Electric power
$P = V I = I^{2} R = \frac{V ^{2}}{R}$
Joule heating
$H = I^{2} R t$
Kirchhoff's junction rule
$\sum I_{in} = \sum I_{o u t}$
Q1MCQJunction rule
Kirchhoff's junction rule expresses conservation of:
- A
  charge
- B
  energy
- C
  momentum
- D
  power
Kirchhoff's loop rule
$\sum I R + \sum ε = 0$
Q1MCQLoop rule
Kirchhoff's loop rule expresses conservation of:
- A
  energy
- B
  charge
- C
  current
- D
  resistance
Wheatstone balance
$\frac{R _{1}}{R _{2}} = \frac{R _{3}}{R _{4}}$
Q1MCQWheatstone
A Wheatstone bridge is balanced when:
- A
  $\dfrac{R_1}{R_2}=\dfrac{R_3}{R_4}$
- B
  $R_1=R_2$
- C
  $R_1 R_2=R_3 R_4$
- D
  $R_1+R_2=R_3+R_4$
Cells in series
$ε_{e q} = \sum ε_{i}, r_{e q} = \sum r_{i}$
Q1MCQCells in series
For cells in series, the total EMF is:
- A
  $\sum\varepsilon_i$
- B
  the average EMF
- C
  $\dfrac{\varepsilon}{n}$
- D
  $0$
Cells in parallel
$ε_{e q} = \frac{\sum ε _{i} / r _{i}}{\sum 1/ r _{i}}$
Q1MCQCells in parallel
For identical cells in parallel, the EMF:
- A
  stays the same, internal resistance drops
- B
  adds up
- C
  halves
- D
  becomes zero
Terminal voltage (discharging)
$V = ε - I r$
Terminal voltage (charging)
$V = ε + I r$
Q1MCQCharging voltage
When a cell is being charged, its terminal voltage is:
- A
  $\varepsilon+Ir$
- B
  $\varepsilon-Ir$
- C
  $\varepsilon$
- D
  $Ir$
Maximum power transfer
$R = r \Rightarrow P_{m a x} = \frac{ε ^{2}}{4 r}$
Q1MCQMax power transfer
Maximum power is delivered to the load when:
- A
  $R=r$
- B
  $R=0$
- C
  $R=\infty$
- D
  $R=2r$
Ammeter shunt
$S = \frac{I _{g} R _{g}}{I - I _{g}}$
Q1MCQAmmeter shunt
The shunt resistance to convert a galvanometer to an ammeter is:
- A
  $\dfrac{I_g R_g}{I-I_g}$
- B
  $\dfrac{V}{I_g}-R_g$
- C
  $\dfrac{I_g R_g}{I}$
- D
  $R_g$
Voltmeter series resistance
$R_{s} = \frac{V}{I _{g}} - R_{g}$
Q1MCQVoltmeter resistance
The series resistance to convert a galvanometer to a voltmeter is:
- A
  $\dfrac{V}{I_g}-R_g$
- B
  $\dfrac{I_g R_g}{I-I_g}$
- C
  $\dfrac{V}{I_g}$
- D
  $R_g$
Metre bridge
$X = (\frac{100 - l}{l}) R$
Q1MCQMetre bridge
In a metre bridge with balance length $l$, the unknown resistance is:
- A
  $\left(\dfrac{100-l}{l}\right)R$
- B
  $\left(\dfrac{l}{100-l}\right)R$
- C
  $lR$
- D
  $\dfrac{R}{l}$
Potential gradient
$x = \frac{V}{L}$
Q1MCQPotential gradient
The potential gradient of a potentiometer wire is:
- A
  $\dfrac{V}{L}$
- B
  $VL$
- C
  $\dfrac{L}{V}$
- D
  $V$
Compare EMFs (potentiometer)
$\frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}$
Q1MCQCompare EMFs
For two cells balanced at lengths $l_1,l_2$, $\dfrac{\varepsilon_1}{\varepsilon_2}$ equals:
- A
  $\dfrac{l_1}{l_2}$
- B
  $\dfrac{l_2}{l_1}$
- C
  $l_1 l_2$
- D
  $1$
Internal resistance (potentiometer)
$r = (\frac{l _{1} - l _{2}}{l _{2}}) R$
Q1MCQInternal resistance
The internal resistance from a potentiometer is:
- A
  $\left(\dfrac{l_1-l_2}{l_2}\right)R$
- B
  $\left(\dfrac{l_1}{l_2}\right)R$
- C
  $\dfrac{R}{l_2}$
- D
  $l_1 R$
Kilowatt-hour
$1 kWh = 3.6 \times 1 0^{6} J$
Cube across body diagonal
$R_{e q} = \frac{5 R}{6}$
Q1MCQCube resistance
The equivalent resistance of a cube of resistors $R$ across a body diagonal is:
- A
  $\dfrac{5R}{6}$
- B
  $\dfrac{7R}{12}$
- C
  $\dfrac{3R}{4}$
- D
  $R$

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Current Electricity formulas

Current Electricity, every formula

Average current

Instantaneous current

Current from drift velocity

Drift velocity

Mobility

Current density

Resistance of a conductor

Resistivity

Ohm's law

Temperature dependence

Series combination

Parallel combination

Voltage division (series)

Current division (parallel)

Electric power

Joule heating

Kirchhoff's junction rule

Kirchhoff's loop rule

Wheatstone balance

Cells in series

Cells in parallel

Terminal voltage (discharging)

Terminal voltage (charging)

Maximum power transfer

Ammeter shunt

Voltmeter series resistance

Metre bridge

Potential gradient

Compare EMFs (potentiometer)

Internal resistance (potentiometer)

Kilowatt-hour

Cube across body diagonal

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