Q1. Two capacitors of 3 µF and 6 µF are connected in series. Find the equivalent capacitance.
1/C = 1/C₁ + 1/C₂ = 1/3 + 1/6 = 2/6 + 1/6 = 3/6
C = 6/3 = 2 µF (series capacitance is smaller than either)
Electrostatic Potential and Capacitance — Class 12
Capacitors store energy in an electric field. Use the calculator to link charge, voltage, capacitance and stored energy, then practise the standard numericals.
Electric potential (V)Work done per unit positive charge in bringing it from infinity to a point: V = W/q. Due to a point charge, V = kQ/r. Unit: volt (V).
Equipotential surfaceA surface on which the potential is the same everywhere; no work is done moving a charge along it, and field lines are perpendicular to it.
Capacitance (C)The charge stored per unit potential difference: C = Q/V. Unit: farad (F). For a parallel-plate capacitor C = ε₀A/d.
Energy storedA charged capacitor stores energy U = ½CV² = ½QV = Q²/2C in its electric field.
Capacitor calculator Interactive
Enter the charge and voltage to read the capacitance and the energy stored (values in micro-units).
Capacitance, C = Q/V—µF
Energy, U = ½QV—µJ
Energy depends on the SQUARE of voltage (½CV²) — doubling the voltage stores four times the energy.
Numericals practice Interactive
Capacitance, energy and combination problems with steps.
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Solved numericals
Q2. A 5 µF capacitor is charged to 200 V. Find the charge and the energy stored.
Q = CV = 5×10⁻⁶ × 200 = 1×10⁻³ C = 1000 µC
U = ½CV² = ½ × 5×10⁻⁶ × 200² = 0.1 J
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Electric potential (point charge) | V = kQ/r | volt (V) |
| Capacitance | C = Q / V | farad (F) |
| Parallel-plate capacitor | C = ε₀A / d | F |
| Energy stored | U = ½CV² = ½QV | joule (J) |
| Capacitors in series | 1/C = 1/C₁ + 1/C₂ | F |
| Capacitors in parallel | C = C₁ + C₂ | F |
Common mistakes & exam wins
- Series capacitors ADD like parallel resistors (reciprocals); parallel capacitors simply add.
- Inserting a dielectric increases capacitance by the dielectric constant K.
- Energy of a capacitor = ½CV² — note the factor of ½ that students often drop.
- No work is done in moving a charge along an equipotential surface.
Frequently asked questions
What is electric potential?
The work done per unit positive charge in bringing it from infinity to a point in an electric field, measured in volts.
What is capacitance?
The ability of a conductor to store charge per unit potential difference, C = Q/V, measured in farads.
How is energy stored in a capacitor?
In the electric field between its plates; the stored energy is U = ½CV² = ½QV = Q²/2C.
What happens to capacitance when a dielectric is inserted?
It increases by a factor equal to the dielectric constant K of the material, because the dielectric reduces the effective field.