Electrostatics & Current Electricity

This unit alone contributes 6–7 marks in NEET. Master the formulas and know every formula-application pair.

Electrostatics

Coulomb's law: F = kq₁q₂/r² where k = 1/(4πε₀) = 9 × 10⁹ N·m²/C². Force is along the line joining charges. In medium: F = kq₁q₂/(εᵣr²).

Electric field: E = kQ/r² (point charge). E inside conductor = 0. E due to infinite sheet = σ/2ε₀ (each side). E between parallel plates = σ/ε₀.

Gauss's law: φ = Q_enclosed/ε₀. Useful for symmetric charge distributions. For spherical shell: E = 0 inside, E = kQ/r² outside.

Potential: V = kQ/r. V inside uniformly charged sphere = constant (= V at surface). Work done = q(V_A - V_B). Equipotential surfaces ⊥ electric field lines.

Capacitors

Parallel plate capacitor: C = ε₀A/d. With dielectric: C = Kε₀A/d. Energy stored: U = ½CV² = Q²/2C = ½QV.

Series: 1/C_total = 1/C₁ + 1/C₂ + ... (same charge Q on each). Equivalent C is smaller than smallest individual C.

Parallel: C_total = C₁ + C₂ + ... (same voltage V on each). Equivalent C is larger than largest.

Energy density: u = ½ε₀E² (energy per unit volume in electric field). When battery disconnected, inserting dielectric → Q constant, V decreases, C increases, U decreases.

Current Electricity

Ohm's law: V = IR. Resistance: R = ρL/A. Temperature dependence: R_T = R₀(1 + αT). Resistivity ρ increases with T for metals, decreases for semiconductors.

Kirchhoff's laws: KCL (junction rule) — sum of currents into junction = sum of currents out. KVL (loop rule) — sum of EMF = sum of potential drops in any closed loop.

Wheatstone bridge: Balanced when P/Q = R/S → zero galvanometer deflection. Used to measure unknown resistance. Meter bridge is its practical application.

Power: P = VI = I²R = V²/R. In series: same I → P proportional to R. In parallel: same V → P proportional to 1/R (higher R → less power dissipated).

EMF & Internal Resistance

Terminal voltage: V = ε - Ir (during discharge). V = ε + Ir (during charging). At open circuit: V = ε (no current, no drop).

Cells in series: ε_total = ε₁ + ε₂, r_total = r₁ + r₂. Best when external resistance >> internal resistance.

Cells in parallel (identical): ε_total = ε, r_total = r/n. Best when external resistance << internal resistance.

Maximum power transfer: Occurs when external resistance = internal resistance (R = r). Power = ε²/4r.

Electrostatics & Current Electricity Formulas

Key Electrostatics Values

k = 9 × 10⁹ N·m²/C²
ε₀ = 8.85 × 10⁻¹² F/m
e = 1.6 × 10⁻¹⁹ C
Electric field infinite sheet: σ/2ε₀
Parallel plates: σ/ε₀

E inside hollow conductor = 0 (shielding). E just outside conductor surface = σ/ε₀ (normal to surface)

Capacitor Formulas

C = Q/V = ε₀A/d
With dielectric: C' = KC
U = ½CV² = Q²/2C
Series: 1/C = 1/C₁ + 1/C₂
Parallel: C = C₁ + C₂

Inserting dielectric with battery connected: V = const, Q increases, C increases, E decreases

Resistance Combinations

Series: R = R₁ + R₂ + ...
Parallel: 1/R = 1/R₁ + 1/R₂
For 2 parallel: R = R₁R₂/(R₁+R₂)
Resistivity: R = ρL/A
Temperature: R_T = R₀(1+αT)

n identical resistors in parallel: R_eq = R/n. In series: R_eq = nR

Power Formulas

P = VI = I²R = V²/R
Energy: E = Pt = VIt
Series → P ∝ R (same I)
Parallel → P ∝ 1/R (same V)
Max power: when R_ext = r (internal)

In household circuits, bulbs in parallel → higher wattage = brighter (more P = V²/R, less R)

Worked Examples

EasyThree capacitors of 2μF, 3μF, and 6μF are connected in series. What is the equivalent capacitance?▾

1/C_eq = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1. Therefore C_eq = 1 μF.

Answer: 1 μF

MediumIn a Wheatstone bridge, P = 10Ω, Q = 20Ω, R = 30Ω. What value of S will balance the bridge?▾

Bridge balanced: P/Q = R/S. 10/20 = 30/S. S = 30 × 20/10 = 60 Ω.

Answer: S = 60 Ω

HardA cell with EMF 2V and internal resistance 0.5Ω is connected to external resistance 1.5Ω. What is the terminal voltage?▾

Current I = ε/(R+r) = 2/(1.5+0.5) = 2/2 = 1A. Terminal voltage V = ε - Ir = 2 - 1×0.5 = 1.5V. Alternatively: V = IR_ext = 1×1.5 = 1.5V ✓

Answer: Terminal voltage = 1.5 V

Mistake DNA

❌ Confusing series and parallel capacitor formulas

Students apply resistor series formula to capacitors. Capacitors in SERIES: 1/C_total = 1/C₁ + 1/C₂ (equivalent C is SMALLER). Capacitors in PARALLEL: C_total = C₁ + C₂ (equivalent C is LARGER).

Fix: Capacitors behave opposite to resistors. Series capacitor: smaller C. Parallel capacitor: larger C.

❌ Saying power is same in series and parallel circuits

In series: same current I flows through all → P = I²R → higher R bulb glows brighter. In parallel: same voltage V across all → P = V²/R → lower R bulb has MORE power, glows brighter. Series vs parallel completely reverses which bulb is brighter.

Fix: Series → high R = high P (bright). Parallel → low R = high P (bright). Completely opposite!

Chapter Intelligence

PYQ Frequency

Capacitor calculations: 2 Q/year
Kirchhoff / Wheatstone: 1–2 Q/year
EMF / terminal voltage: 1 Q/year
Gauss's law: 1 Q/year

2026 Prediction

High: Capacitor combination + energy
Expected: Meter bridge / Wheatstone
Watch: Dielectric effect on capacitor

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