NEB Class 11 • Physics • Focused Revision

Capacitors Study Guide: NEB 11 Physics

Turn capacitor formulas into a decision tree: identify geometry, connection, fixed variable and required energy form before calculating.

Seven-session capacitance plan
Battery-connected versus isolated checks
Networks, energy, graphs and timed test

Capacitance links stored charge to potential difference.

Revision boundary

Identify the constraint before the formula

Use the CDC secondary curriculum and CDC Physics Grade 11 page. Read the paired Capacitors concept guide and OpenStax capacitance treatment.

A strong solution begins by naming: single or network, geometry or circuit, battery-connected or isolated, and fixed Q or V.

Knowledge map

Use four linked layers

Definition

C=Q/V and units.

Geometry

C=εA/d and dielectric.

Network

Equal voltage in parallel, equal charge in series.

Energy

½CV², Q²/(2C), ½QV and field energy.

Seven sessions

A spaced capacitor plan

Session	Focus	Exit evidence
1	Definition, prefixes, plate charge	Ten unit cards
2	Parallel-plate geometry	Six scaling problems
3	Dielectric constraints	Two comparison tables
4	Series networks	Six equal-charge solutions
5	Parallel and mixed networks	Six reductions
6	Energy and graphs	Eight formula-choice tasks
7	Timed integrated set	80% without repeated constraint error

Scaling drills

Predict ratios before numbers

Geometry change

A→3A and d→2d gives C′/C=3/2. If isolated, Q fixed, V becomes 2/3 of original and U becomes 2/3. If battery-connected, V fixed, Q and U become 3/2.

Dielectric

Fully inserting κ=5 multiplies C by 5. With battery connected Q and U multiply by 5. When isolated, V and U divide by 5.

Write a fixed-variable column before applying Q=CV or energy equations.

Network method

Reduce topology, then expand charge and voltage

Mark nodes to identify true parallel branches.
Find unmistakable series groups.
Reduce one group at a time.
Find total charge from C_eqV.
Expand: series group shares Q; parallel group shares V.
Check charge and voltage sums.

Mixed network

3 μF and 6 μF in series give 2 μF; in parallel with 4 μF the total is 6 μF. Across 12 V, total charge is 72 μC. The 4 μF branch has 48 μC; the series branch has 24 μC on each capacitor, with 8 V and 4 V drops.

Energy choice

Match the formula to what remains fixed

Known or fixed	Useful form	Trend when C increases
V	U=½CV²	U increases
Q	U=Q²/(2C)	U decreases
Q and V	U=½QV	Direct calculation

Voltage doubled

For fixed C, Q doubles but U quadruples because energy depends on V².

On V–Q axes, label slope and area before interpreting. Use PhET Capacitor Lab after predicting.

Error log

Repair the first network or constraint mistake

Error	Code	Repair
Added series C directly	topology	Use reciprocal sum
Gave same V in series	rule	Use equal Q
Kept Q and V fixed together	constraint	Name battery status
Used μF as F	unit	Convert prefix
Used wrong energy form	variables	Circle fixed Q or V

Forty-minute checkpoint

Integrated readiness tasks

Define capacitance and plate charge.
Calculate parallel-plate C and scaling.
Compare dielectric insertion under both constraints.
Solve two series and two parallel networks.
Reduce a mixed network and expand values.
Calculate energy three ways.
Interpret Q–V and V–Q graphs.
Explain applications and retained-energy safety.

Equivalent bounds are checked.
Prefixes are converted.
Series Q and parallel V rules are visible.
Battery status is stated.
Energy formula matches fixed variables.
Final units are F, C, V or J as appropriate.

For online or physical NEB tuition, call 9846662070.

Frequently asked questions

Questions about studying capacitors

What should I identify first?

Decide whether the problem is geometry or a network, then state battery-connected or isolated and the fixed variable.

How do I remember network rules?

Parallel branches share voltage and capacitances add; series elements share charge and reciprocals add.

How can I check an equivalent capacitance?

Parallel equivalent must exceed the largest member; series equivalent must be below the smallest.

Why does dielectric energy change differently?

With fixed V the battery supplies charge and energy; with fixed Q the increased capacitance lowers voltage and stored energy.

What score shows readiness?

Aim for 80% on a fresh mixed set with no repeated topology, prefix, constraint or energy-form error.

Where can I get capacitor tuition?

Call 9846662070 for current online or physical NEB tuition schedules and fees.

References and next steps

Sources and related study guides

Use the Capacitors Practice Set and revisit potential and energy. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Constraint workbook

Four one-change thought experiments

Start from Q, V, C and U. Change one condition at a time: disconnect battery, insert dielectric, halve separation, reconnect to the same battery. After each step, write which quantity is constrained and calculate ratios before values.

Two-step sequence

A charged capacitor is disconnected, then κ=4 inserted: C×4, Q fixed, V/4 and U/4. Reconnect it to its original voltage source: V returns to initial, Q becomes four times original and U becomes four times original.

Sequence matters because the battery can exchange charge and energy. Draw a timeline rather than treating every formula simultaneously.

Worked study workbook

Eight drills for topology and constraints

1. Prefix discipline

470 nF=0.470 μF=4.70×10⁻⁷ F. At 9 V it stores Q≈4.23 μC.

2. Geometry ratio

κ doubles, area halves and separation quarters: C′/C=2×0.5/(0.25)=4.

3. Isolated plate motion

Doubling separation halves C. With fixed Q, V doubles and U doubles; external work is stored in the field.

4. Connected plate motion

With V fixed, doubling separation halves C, Q and U. Charge returns to the battery and complete energy accounting includes mechanical work.

5. Series voltage

2 μF and 4 μF in series across 12 V carry equal Q=16 μC; drops are 8 V and 4 V, larger across the smaller capacitance.

6. Parallel charge

The same elements in parallel each have 12 V; charges are 24 and 48 μC and total 72 μC.

7. Energy consistency

For a reduced network, calculate U_total=½C_eqV² and compare with the sum of ½CᵢVᵢ² after expanding. They should agree in the ideal model.

8. Graph choice

Q–V slope is C; V–Q slope is 1/C. The triangular area to a point equals ½QV on either correctly labelled linear graph.

Spaced study method

On day 1 classify ten problems by topology and constraint without solving. On day 2 calculate them. On day 4 expand mixed networks. On day 7 explain energy changes orally. Retest recurring errors with different circuit drawings so node logic, not visual familiarity, controls the method.

Use a four-column error log: first wrong decision, correct rule, contrast problem and retest date. Typical codes are prefix, topology, fixed variable, equal-Q/equal-V rule, equivalent bound and energy form.

Timed revision paper

Thirty-minute integrated set

Convert 220 pF, 47 nF and 10 μF to farads.
Find C, Q and E for a specified parallel plate.
Apply simultaneous area, separation and dielectric changes.
Analyse dielectric insertion with the battery connected.
Repeat after disconnection.
Reduce a mixed three-capacitor network.
Find every branch charge and voltage.
Compare total energy with sum of element energies.
Interpret Q–V and V–Q slopes and areas.
Explain retained-energy safety.

Mark topology before algebra. For a mixed network, redraw equivalent steps and then reverse them to expand values. Check that charge entering a parallel group equals the sum of branch charges and that series voltage drops equal the source.

For a dielectric or moving-plate problem, make a before/after table with C, Q, V and U. Circle the fixed quantity. Use ratio reasoning first, then calculate absolute values. Explain energy exchange with the battery, field force or external agent.

After the paper, write one reverse-design question and one error-diagnosis question. Retest in three days with a differently drawn but electrically identical network so node structure, not picture recognition, controls your method.

Weekly transfer: take one mixed network and solve it forward from equivalent capacitance to individual values. Then hide the original source voltage and reconstruct it from branch data. Replace one capacitor with a dielectric-adjusted value and repeat. Finally disconnect the battery and change plate separation, using a before/after table. This sequence forces node logic, constraints and energy accounting to work together instead of remaining separate formula chapters.

Before finishing, explain aloud why the same dielectric insertion increases stored energy at fixed voltage but decreases it at fixed charge. Name the battery or mechanical agent responsible for the difference and verify both results with the appropriate energy equation.

Then repeat the explanation independently tomorrow.

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