NEB Class 11 • Physics • Worked Practice

Capacitors Practice Set: NEB 11 Physics

Solve graduated capacitor problems where every answer names topology, fixed variable, equivalent bounds and energy meaning before calculator work.

Concept and scaling rounds
Worked series, parallel and mixed networks
Dielectric, energy, graph and timed tasks

Capacitance links stored charge to potential difference.

Source check

Practise within a clear capacitor model

Use the CDC secondary curriculum and CDC Physics Grade 11 page. Review Capacitors and the study guide. Equations align with OpenStax capacitance.

Round 1 • Concepts

Answer before arithmetic

Define capacitance and farad.
Why does an ideal charged capacitor have zero net charge?
Which geometry changes increase parallel-plate C?
Why does a dielectric increase C?
What is equal in series capacitors?
What is equal in parallel capacitors?
Why is stored energy one-half QV?
Why can a disconnected capacitor remain dangerous?

Round 2 • Geometry

Worked parallel-plate problems

1. Capacitance

A=0.050 m² and d=2.0 mm in vacuum give C≈(8.85×10⁻¹²)(0.050)/0.002=2.21×10⁻¹⁰ F=221 pF.

2. Charge and field

At 500 V, Q=CV≈1.11×10⁻⁷ C. Approximate uniform field E=V/d=2.5×10⁵ V/m.

3. Scaling

Area doubles, separation triples and dielectric κ=4 fills the gap: C′/C=4×2/3=8/3.

Round 3 • Constraints

Battery connected versus isolated

Connected

A 5 μF capacitor at 10 V receives κ=3. C becomes 15 μF, V remains 10 V, Q rises from 50 to 150 μC, and U rises from 0.25 to 0.75 mJ.

Isolated

The same initial capacitor is disconnected before insertion. Q remains 50 μC, C becomes 15 μF, V falls to 3.33 V and U falls from 0.25 mJ to about 0.0833 mJ.

Explain energy exchange: the battery supplies energy in the connected case; field forces can do mechanical work in the isolated case.

Round 4 • Networks

Reduce and expand values

Two in parallel

4 μF and 8 μF across 15 V give C_eq=12 μF, Q_total=180 μC, with branch charges 60 and 120 μC.

Two in series

4 μF and 8 μF across 15 V give C_eq=8/3 μF and Q=40 μC on each. Drops are 10 V and 5 V.

Mixed network

2 μF and 3 μF in parallel give 5 μF; in series with 10 μF the total is (5×10)/(15)=10/3 μF. Across 12 V, series charge is 40 μC. The 5 μF group has 8 V and the 10 μF element 4 V. Inside the parallel group, charges are 16 and 24 μC.

Round 5 • Energy and graphs

Choose variables before the formula

Energy at fixed voltage

C=20 μF, V=30 V gives U=½CV²=9.0 mJ.

Energy at fixed charge

Q=60 μC and C=12 μF give U=Q²/(2C)=0.15 mJ.

Graph

A Q–V line has slope 5 μC/V, so C=5 μF. At 20 V, Q=100 μC and area under the line is ½QV=1.0 mJ.

Use PhET Capacitor Lab after predicting.

Marking grid

Diagnose the first failed decision

Evidence	Mark
Topology or geometry identified	1
Battery status and fixed variable	1
Prefixes converted	1
Correct C relation	1
Charge/voltage expansion	1
Equivalent bounds checked	1
Energy and unit interpreted	1

Timed challenge

Forty-minute mixed set

Find C, Q and E for a parallel plate.
Apply simultaneous A, d and κ changes.
Compare connected and isolated dielectric insertion.
Solve two-capacitor series and parallel circuits.
Reduce a three-capacitor mixed network.
Find every individual Q and V.
Calculate total and element energies.
Interpret a V–Q graph.
Explain retained-charge safety.

Check series equivalent below the smallest and parallel above the largest. Sum series voltage drops and parallel branch charges. For online or physical NEB tuition, call 9846662070.

Frequently asked questions

Questions about the capacitor practice set

What should I write before solving?

Identify geometry or network, mark nodes, state battery-connected or isolated, and circle the fixed quantity.

How do I expand a reduced network?

Use equal charge through series groups and equal voltage across parallel branches, checking sums at every step.

Which energy formula is safest?

Use the form containing known or fixed variables: ½CV², Q²/(2C), or ½QV.

How do I check a mixed-network answer?

Apply equivalent bounds, voltage sums, charge sums and total energy consistency.

What score shows readiness?

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

Where can I get help with capacitors?

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

References and next steps

Sources and related study guides

Review the Capacitors Study Guide and Electric Potential after marking. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Reverse design

Choose a network for a target capacitance

Using 6 μF capacitors, two in parallel make 12 μF, two in series make 3 μF, and three in series make 2 μF. To make 9 μF, place a series pair (3 μF) in parallel with one 6 μF capacitor.

Voltage rating reasoning

Ideal equal capacitors in series share voltage equally, but real tolerance and leakage can make division unequal. Never infer safe high-voltage design from introductory ideal equations; follow rated components and engineering safety practice.

Reverse problems test topology selection rather than recognition of a pre-drawn circuit.

Additional worked round

Six multi-step capacitor problems

1. Find plate area

A vacuum capacitor has C=88.5 pF and d=1.0 mm. A=Cd/ε₀=(88.5×10⁻¹²)(10⁻³)/(8.85×10⁻¹²)=0.010 m².

2. Find dielectric constant

The same geometry rises from 100 pF to 450 pF when fully filled, so κ=C/C₀=4.5 in the ideal model.

3. Three in series

2, 3 and 6 μF in series give 1/C_eq=1/2+1/3+1/6=1, so C_eq=1 μF. Across 12 V, each has Q=12 μC and drops are 6, 4 and 2 V.

4. Bridge-looking network check

Mark electrical nodes before declaring series or parallel. Components are parallel only if both ends share the same two nodes; series elements share a node with no other branch. A drawing that looks side by side may not be parallel.

5. Energy after reconnection

A capacitor C charged to V is disconnected and connected in parallel to identical uncharged C. Charge conservation gives final voltage V/2. Final stored energy is 2×½C(V/2)²=¼CV², half the initial ½CV²; the missing energy is dissipated or radiated during redistribution in a real connection.

6. Force-work interpretation

An isolated capacitor attracts its plates. Allowing separation to decrease raises C and lowers Q²/(2C); field energy becomes mechanical energy or external work. Holding plates fixed prevents that mechanical change.

Challenge questions

Design 5 μF using 10 μF elements.
Find all Q and V in a 4 μF series with a 6 μF∥3 μF branch.
Compare energy before and after κ=3 insertion under both constraints.
Draw Q–V graphs for C and 2C and compare slopes and energy areas at fixed V.
Explain why voltage rating cannot be inferred from capacitance alone.

After marking, change battery status or topology and solve again. Keep equivalent bounds, charge conservation, voltage sums and total-energy checks visible on every page.

Experimental and safety audit

Evaluate a low-voltage capacitance investigation

A school setup may estimate capacitance from known charge and measured voltage or study how C varies with area and separation using an approved sensor. Measure plate overlap, separation and dielectric thickness carefully; keep plates parallel and account for edge effects when separation is not small.

Stray capacitance from leads, instruments and nearby objects can be comparable to small pF values. A zero or background reading should be measured and reported. Repeated placement reveals mechanical variation. Do not claim exact ε from one noisy reading.

Use only teacher-approved low-voltage equipment. Discharge through an appropriate resistor and verify voltage before handling. Never short a charged capacitor with metal and never open mains-powered equipment.

Data interpretation

Plot C against A at fixed d for an expected straight line, or C against 1/d at fixed A. The gradient estimates εA or ε depending on chosen axes. A nonzero intercept can represent stray capacitance. Curvature may show fringing, plate nonparallelism or unreliable spacing.

Write the graph equation in y=mx+c form before extracting a material or geometric quantity. State units of gradient and distinguish model disagreement from random scatter.

Final audit: for every numerical answer write one bound or conservation check. Equivalent capacitance must respect series/parallel limits, series drops must equal source voltage, parallel branch charges must sum to total, and element energies must sum to network energy. If a dielectric or plate motion occurs, identify the agent exchanging energy. Retest one failed problem after forty-eight hours with the battery status changed.

Preserve the working, units and checks for spaced review after one week.

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