Class 12 · Chapter 2
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
8 formulas across 3 topics in Electrostatic Potential & Capacitance.
Updated 2026-07-05 · v1.0.0
Potential is potential energy per unit charge, with zero at infinity. Unlike field, it is a scalar — add potentials with signs, no vectors.
V = (1/4πε₀) q/r
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| V | electric potential | V (= J/C) | [ML²T⁻³A⁻¹] |
| q | source charge (with sign) | C | [AT] |
| r | distance from the charge | m | [L] |
Valid when
Common mistakes
E = −dV/dr; V(B) − V(A) = −∫ E·dl
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| E | electric field | V/m | [MLT⁻³A⁻¹] |
| dV/dr | potential gradient | V/m | [MLT⁻³A⁻¹] |
Valid when
Common mistakes
U = (1/4πε₀) q₁q₂/r (pair); sum over all pairs for a system
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| U | electrostatic potential energy | J | [ML²T⁻²] |
| r | separation of a charge pair | m | [L] |
Valid when
Common mistakes
Worth remembering
A capacitor stores charge at a cost of potential; C = Q/V depends only on geometry and the dielectric. Series and parallel are the reverse of resistors.
C = ε₀A/d; with dielectric C = Kε₀A/d
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| C | capacitance | F | [M⁻¹L⁻²T⁴A²] |
| A | plate area | m² | [L²] |
| d | plate separation | m | [L] |
| K | dielectric constant of the medium | dimensionless | [M⁰L⁰T⁰] |
Valid when
Common mistakes
Series: 1/C(eq) = Σ 1/Cᵢ; Parallel: C(eq) = Σ Cᵢ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| C(eq) | equivalent capacitance | F | [M⁻¹L⁻²T⁴A²] |
Valid when
Common mistakes
With battery connected: Q → KQ, V same; Disconnected: V → V/K, Q same
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| K | dielectric constant | dimensionless | [M⁰L⁰T⁰] |
Valid when
Common mistakes
Worth remembering
Charging a capacitor stores energy in the field between the plates — half of what the battery supplies; the other half is lost as heat.
U = ½ CV² = ½ QV = Q²/2C
Integrating dW = (q/C)dq as charge builds from 0 to Q
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| U | energy stored | J | [ML²T⁻²] |
| Q | charge | C | [AT] |
| V | voltage across the capacitor | V | [ML²T⁻³A⁻¹] |
Valid when
Common mistakes
V = (C₁V₁ + C₂V₂)/(C₁ + C₂); heat lost = ½ C₁C₂(V₁ − V₂)²/(C₁ + C₂)
Charge conservation on connecting the plates
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| V | common potential after connection | V | [ML²T⁻³A⁻¹] |
Valid when
Common mistakes
Worth remembering
NEET focuses on C combinations, dielectric shifts and energy; JEE Advanced adds partial dielectrics, force on plates, and multi-capacitor charge-sharing networks.
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