Capacitors: NEB Class 11 Physics Guide

Curriculum boundary

What capacitor mastery connects

The CDC secondary curriculum includes capacitance, capacitor combinations and energy; check the CDC Physics Grade 11 page. This guide follows OpenStax capacitors and capacitance.

Review Electric Potential and Electric Field.

Physical meaning

Capacitance is a device property in the linear model

A capacitor has two conductors separated by an insulator or vacuum. Charging moves electrons from one conductor to the other, leaving equal and opposite plate charges ±Q while total capacitor charge remains zero. C=Q/V tells how much magnitude Q is stored on either plate per voltage difference.

The farad is C/V. Practical values often use μF, nF or pF. A 20 μF capacitor at 12 V stores Q=CV=240 μC.

Parallel plates

Read C=εA/d as geometry, not force

For large plates with separation small relative to dimensions and negligible edge effects, C=εA/d. Larger area increases capacitance; larger separation decreases it. ε=ε₀ in vacuum and ε=κε₀ for an ideal dielectric filling the gap.

Dielectric response

State whether the battery remains connected

An ideal dielectric polarises and increases capacitance by factor κ when it fills the gap. What happens to Q, V and U depends on the constraint.

Energy changes include work by the dielectric force and/or battery. Do not compare formulas without naming the fixed quantity.

Combinations

Use charge and voltage rules to derive equivalents

Parallel capacitors share the same voltage and their charges add, so C_eq=ΣC. Series capacitors carry equal charge magnitude and their voltage drops add, so 1/C_eq=Σ1/C.

Series equivalent is smaller than the smallest capacitor; parallel equivalent is larger than the largest. Use these as instant checks.

Energy storage

Average charging voltage gives the factor one-half

As charge builds from 0 to Q, capacitor voltage rises from 0 to V. The average is V/2 in a linear capacitor, so work and stored energy are U=½QV. Equivalent forms follow from Q=CV.

For a vacuum field, energy density is u=½ε₀E². Capacitor energy is in the electric field, not “inside the charge” alone.

Graph interpretation

Use area under V–Q or Q–V carefully

On a V-versus-Q graph, gradient is 1/C and area under the line from 0 to Q is U. On a Q-versus-V graph, gradient is C and area under the line is also U because ∫Q dV=½CV² for the linear case. Label axes before reading slope.

Use PhET Capacitor Lab: Basics after predicting geometry and dielectric changes.

Applications and safety

Stored energy can remain after disconnection

Capacitors smooth power supplies, filter signals, set timing and release energy quickly in flashes or medical devices. Charged capacitors—especially high-voltage or large-capacitance types—can retain dangerous energy after power is removed. Never short or open equipment capacitors; classroom work must use teacher-approved low-energy components and safe discharge procedures.

Exam readiness

Common mistakes and practice tasks

• Q means magnitude on one plate.
• C is not charge and unit is farad.
• Convert μF and mm before equations.
• Series capacitors share charge.
• Parallel capacitors share voltage.
• State battery-connected or isolated.
• Choose the energy form matching fixed variables.
• Check equivalent bounds.

1. Calculate a parallel-plate capacitance.
2. Compare geometry changes.
3. Analyse dielectric insertion in both constraints.
4. Solve series and parallel networks.
5. Find individual charges and voltages.
6. Calculate stored energy and graph area.

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References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• CDC Nepal: Secondary Curriculum
• OpenStax: Capacitors and Capacitance
• OpenStax: Capacitors and Dielectrics
• OpenStax: Series and Parallel Capacitors
• OpenStax: Stored Energy

Continue with the Capacitors Study Guide and practice set. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Physical transfer

Mechanical forces and changing separation

Oppositely charged plates attract. If an isolated capacitor’s plate separation decreases, C increases while Q stays fixed, so V and field energy decrease; the electric force can do mechanical work. If a battery keeps V fixed, charge flows and battery energy exchange changes the accounting.

This explains why memorising “larger C means larger energy” is unsafe: the result depends on fixed Q or fixed V.

Geometry extensions

Partial dielectrics and non-ideal limits

If a dielectric fills only part of the plate area, the regions can be modelled as parallel capacitors because they share the same voltage. If layers are stacked along the field direction, they behave like series capacitors because the same free plate charge passes through the displacement structure while voltage drops add.

Battery energy accounting

When a battery charges a capacitor from zero to V, the battery transfers energy QV=CV². The ideal capacitor stores ½CV²; in a simple resistive charging path the remaining half is dissipated as heat. Exact transient behaviour belongs to circuit analysis, but the energy balance prevents the mistaken claim that all battery work is stored.

Breakdown and ratings

Real dielectrics fail above a material- and geometry-dependent electric field. Capacitance equations do not guarantee safe operation. Voltage ratings, polarity for electrolytic types, temperature and manufacturing tolerance matter. Never connect unknown capacitors to mains power.

Dimensional check

From C=εA/d, ε must have unit F/m. From U=½CV², F·V²=(C/V)V²=C·V=J. These checks catch missing conversion factors and incorrect energy powers.