Quick Revision Current Electricity

⚡ Electric Current & Drift

• I = dQ/dt = nAev_d | Units: Ampere

• v_d = eEτ/m | Order: ~10⁻⁴ m/s

• J = I/A = nev_d = σE (vector form)

• Current direction = +ve charge flow (opposite to e⁻)

🔋 Ohm's Law & Resistance

• V = IR | R = ρL/A | ρ = m/(ne²τ)

• Metals: R increases with T (R_T = R₀(1+αT))

• Semiconductors: R decreases with T

• Series: R_s = ΣRᵢ | Parallel: 1/R_p = Σ(1/Rᵢ)

🔋 EMF & Cells

• V = ε − Ir (discharging) | V = ε + Ir (charging)

• I = ε/(R+r)

• Max power: R = r → P_max = ε²/4r

• n cells series: ε_eff = nε, r_eff = nr

• n cells parallel: ε_eff = ε, r_eff = r/n

• Mixed m×n: I = mnε/(mR+nr)

🔁 Kirchhoff's Laws

• KCL: ΣI_in = ΣI_out (conservation of charge)

• KVL: ΣV = 0 in any closed loop (conservation of energy)

• KVL sign: Cross R in I direction → −IR | Opposite → +IR

• Negative current means assumed direction was wrong

⚖ Wheatstone & Potentiometer

• Wheatstone balance: P/Q = R/S (I_g = 0)

• Meter Bridge: S = R(100−l)/l

• Potentiometer: ε₁/ε₂ = l₁/l₂

• Internal r: r = R(l₁−l₂)/l₂

• Potentiometer > voltmeter: draws zero current at balance

⚡ Power & Heating

• P = VI = I²R = V²/R

• H = I²Rt = Pt = V²t/R

• 1 kWh = 3.6×10⁶ J

• Series (same I): higher R → more power

• Parallel (same V): lower R → more power

• Bulb R = V²/P (lower P-rating = higher R)

🔬 RC Circuits (JEE)

• τ = RC | At t=0: C → wire | At t→∞: C → open

• Charging: q = Cε(1−e^(−t/RC))

• Discharging: q = q₀e^(−t/RC)

• Energy: ½ stored in C, ½ dissipated in R (always)

📏 Key Dimensions

R: [M¹L²T⁻³A⁻²]

ρ: [M¹L³T⁻³A⁻²]

V: [M¹L²T⁻³A⁻¹]

σ: [M⁻¹L⁻³T³A²]

J: [A¹L⁻²]

P: [M¹L²T⁻³]

🔬

5 Must-Remember Facts (1) Terminal V = EMF only when I = 0. (2) Negative current ≠ error — just direction reversal. (3) Stretched wire: n× length → n² × resistance. (4) In series, lower P-rating bulb glows brighter. (5) RC at t=0: capacitor is a wire; at t→∞: open circuit.

Click card to flip. Use arrows to navigate.

Question

What is the relation between drift velocity and electric field?

Click to see answer

Answer

v_d = eEτ/m = μE
where μ = eτ/m = mobility

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🎯

Formula Dump — Print-Ready Format These are all the formulas you need to carry in your head into the exam. Grouped by topic. Scan through these 15 minutes before the exam.

⚡ Fundamentals

I = dQ/dt = nAev_d

v_d = eEτ/m | J = σE

R = ρL/A | ρ = m/(ne²τ)

R_T = R₀(1+αΔT)

🔋 EMF & Cells

V = ε − Ir (discharge)

V = ε + Ir (charge)

n series: ε_s = nε, r_s = nr

n parallel: ε_p = ε, r_p = r/n

m×n mixed: I = mnε/(mR+nr)

⚡ Power & Heat

P = VI = I²R = V²/R

H = I²Rt | P_max = ε²/4r

Efficiency η = R/(R+r)

1 kWh = 3.6×10⁶ J

🔌 Circuits

Series: R = R₁+R₂+...

Parallel: 1/R = 1/R₁+1/R₂+...

KCL: ΣI = 0 at junction

KVL: ΣV = 0 in loop

⚖ Instruments

Wheatstone: P/Q = R/S

Meter Bridge: S = R(100-l)/l

Pot EMF: ε₁/ε₂ = l₁/l₂

Pot int.r: r = R(l₁-l₂)/l₂

🔬 RC Circuits (JEE)

τ = RC

q(t) = Cε(1-e^(-t/RC))

I(t) = (ε/R)e^(-t/RC)

t=0: C=wire | t→∞: C=open

Memory Tricks & Mnemonics

🏎 "VIR" Triangle

V = IR. Cover what you need: Cover V → V = IR. Cover I → I = V/R. Cover R → R = V/I. Draw the triangle. Never forget Ohm's Law.

🔋 "DICE" for Terminal Voltage

Discharging: V = ε − Ir (Drops). Charging: V = ε + Ir (Climbs). D = Drops, C = Climbs.

📐 "Stretch = Square" Rule

Wire stretched to n times → R becomes n² times. "Stretch it by 3, multiply R by 9 (3²)." Square the stretch factor.

💡 "Lower Watt, Higher R" for Bulbs

At rated voltage: R = V²/P. Lower P → Higher R. Series: same I → higher R glows brighter. "Low watt bulb is the champion in series."

🔁 "KCL = Crowd" & "KVL = Journey"

KCL: At a junction, it's like a crowd — people entering = people leaving. KVL: Going around a loop is like a journey — you start and end at the same energy level. Net gain = 0.

⏱ "RC = τ" — The 63% Rule

At t = τ = RC: capacitor reaches 63% of final charge (1 − 1/e ≈ 0.63). At t = 5τ: essentially fully charged (99.3%). "One τ = 63%, Five τ = done."

🌉 "Wheatstone = No Bridge Crossing"

At balance: no current "crosses the bridge" (galvanometer). P/Q = R/S means both sides climb at the same ratio — no need to cross.

🎸 "Potentiometer is Perfect, Voltmeter is Not"

Potentiometer: measures true EMF because it takes nothing from the cell. Voltmeter: takes current → reads terminal voltage. "Perfect instrument takes nothing."

Quick Revision

Memory Tricks & Mnemonics

Pre-Exam Checklist — Current Electricity

Chapter Complete!