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Current Electricity formula sheet

Every formula in the Current Electricity chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 27 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Current, drift velocity and resistance

Electric current
4× asked, last 2024
I=dqdt,q=∫I dt,dNdt=IeI=\frac{dq}{dt},\qquad q=\int I\,dt,\qquad \frac{dN}{dt}=\frac Ie
qq = area under II–tt. Linear II: average current × time.
Drift velocity and mobility
8× asked, last 2026
I=neAvd,vd=eEτm,μ=vdE=eτmI=neAv_d,\qquad v_d=\frac{eE\tau}m,\qquad \mu=\frac{v_d}E=\frac{e\tau}m
Fixed VV: vd∝1/Lv_d\propto1/L, not on AA. Fixed II: vd∝1/Av_d\propto1/A. 1 mm2=10−6^2=10^{-6} m2^2.
Current density and conductivity
5× asked, last 2022
J=IA=nevd,J⃗=σE⃗,σ=1ρ=ne2τm=neμJ=\frac IA=nev_d,\qquad \vec J=\sigma\vec E,\qquad \sigma=\frac1\rho=\frac{ne^2\tau}m=ne\mu
Tilted J⃗\vec J: I=JAcos⁡θI=JA\cos\theta.
Resistance and resistivity
14× asked, last 2025
R=ρLA,ρ=mne2τR=\frac{\rho L}A,\qquad \rho=\frac m{ne^2\tau}
Fixed volume: R=ρL2/V∝1/r4R=\rho L^2/V\propto1/r^4. Radial between coaxial cylinders: ρln⁡(b/a)/2πl\rho\ln(b/a)/2\pi l.
Stretching a wire
11× asked, last 2024
L→nL: R′=n2R,r→rn: R′=n4RΔRR≈2ΔLL\begin{aligned}&L\to nL:\ R'=n^2R,\qquad r\to\frac rn:\ R'=n^4R\\&\frac{\Delta R}R\approx\frac{2\Delta L}L\end{aligned}
Volume constant. 10% stretch: 21%. "Increased by nn times": (n+1)L(n+1)L.
Temperature dependence
12× asked, last 2026
RT=R0(1+α ΔT)R_T=R_0(1+\alpha\,\Delta T)
Metals α>0\alpha>0, semiconductors <0<0. Series: α=(R1α1+R2α2)/(R1+R2)\alpha=(R_1\alpha_1+R_2\alpha_2)/(R_1+R_2).
Ohm's law
4× asked, last 2024
V=IR,R=slope of V–IV=IR,\qquad R=\text{slope of }V\text{–}I
On an II–VV graph R=1/slopeR=1/\text{slope}. Non-ohmic: R=V/IR=V/I.

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20 more formulas 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.

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Resistor combinations and networks

  • Series and parallel29×
  • Wire bent into a loop7×
  • Cube of resistors15×
  • Infinite ladder1×

Kirchhoff's laws and meters

  • Kirchhoff's laws36×
  • Ammeter and voltmeter11×
  • Capacitor in a DC circuit5×

Cells, emf and internal resistance

  • EMF and terminal voltage13×
  • Cells in series8×
  • Cells in parallel12×
  • Mixed grouping
  • Maximum power transfer2×

Electrical power and heating

  • Joule heating19×
  • Rated bulbs8×
  • Heating time with two coils2×
  • Energy units; transmission5×

Bridges, divider and potentiometer

  • Wheatstone bridge11×
  • Metre bridge13×
  • Potential divider6×
  • Potentiometer (dropped 2024)20×

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About 245 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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