NEB Class 11 • Physics • Worked Practice

DC Circuits Practice Set: NEB 11 Physics

Solve from conservation, not visual familiarity. The set moves from short concept checks to mixed networks, real sources, loops, meters and practical evaluation.

Questions first, worked reasoning second
Bounds and conservation checks
Timed transfer and error-repair method

Node and loop rules turn a drawing into conservation equations.

Preparation

Build on the concept and study guides

Check the official CDC Physics Grade 11 page, then review the DC Circuits concept guide and DC Circuits Study Guide. The OpenStax Ohm’s-law section and Kirchhoff section provide institutional comparison.

Use SI units: amperes, volts, ohms, watts and seconds. When a source has internal resistance, distinguish emf, terminal voltage and load voltage. Treat ideal wires as single-potential nodes and real meter limitations only when the question asks for them.

Round 1

Concept checks with compact answers

Does current decrease after a resistor? No in one steady series path; charge flow rate is equal, while energy per coulomb decreases.
Can two side-by-side drawn resistors be non-parallel? Yes; they are parallel only if both ends share the same two nodes.
Which equivalent is larger? Series exceeds every member; parallel is less than the smallest positive member.
What does a negative branch current mean? Actual flow is opposite to the chosen arrow.
Why does a voltmeter go in parallel? It compares two-point potential difference and ideally draws negligible current.
Why does an ammeter go in series? The branch current must pass through it; ideal resistance is nearly zero.
Can voltage exist with zero current? Yes, for example across an open circuit or unloaded source.
Can current exist with zero resistance? An ideal model would be a short circuit; real sources and wires limit current and may overheat.

For every answer, name charge conservation, energy conservation, node equality or an element model. Avoid explanation by formula alone.

Round 2

Resistor networks: worked examples

1. Series network

3 Ω, 5 Ω and 12 Ω are in series across 20 V. R_eq=20 Ω, I=1.0 A and drops are 3 V, 5 V and 12 V. Their sum is 20 V. Powers 3 W, 5 W and 12 W sum to source power 20 W.

2. Parallel network

6 Ω, 12 Ω and 4 Ω are across 12 V. Currents are 2 A, 1 A and 3 A; total 6 A. Thus R_eq=12/6=2 Ω, below 4 Ω. Total power is 72 W.

3. Mixed network

A 5 Ω resistor is in series with 10 Ω∥15 Ω. Parallel equivalent is 6 Ω; total 11 Ω. Across 22 V, total current is 2 A. The series resistor drops 10 V, leaving 12 V across the branches. Currents 1.2 A and 0.8 A add to 2 A.

4. Reverse design

A 12 V supply should deliver 3 A to a network containing 2 Ω in series with an unknown parallel equivalent. Total must be 4 Ω, so the parallel part must be 2 Ω. Two 4 Ω resistors in parallel satisfy that requirement.

Redraw after every reduction and expand values in reverse order. Never assign the source voltage to a component unless it shares both source nodes.

Round 3

Emf, terminal voltage and maximum-power reasoning

5. Loaded cell

A cell ε=2.0 V and r=0.50 Ω powers R=3.5 Ω. I=2.0/(4.0)=0.50 A. Terminal voltage is 2.0−0.25=1.75 V, equal to IR. Source power εI=1.0 W; load power I²R=0.875 W; internal loss I²r=0.125 W.

6. Infer internal resistance

An open-circuit reading is 1.60 V. When current is 0.80 A, terminal voltage becomes 1.44 V. Assuming the simple model, r=(ε−V)/I=(0.16)/0.80=0.20 Ω.

7. Charging sign

A 12 V battery being charged at 2 A has 13 V across its terminals. With V=ε+Ir, r=(13−12)/2=0.50 Ω. State that current enters the positive terminal; otherwise the sign is ambiguous.

Challenge: for fixed ε and r, load power P=ε²R/(R+r)² is greatest in the simple model when R=r. Derive by comparing nearby values or calculus if studied. Do not treat this as a safe operating rule; real sources have current and thermal limits.

Round 4

Kirchhoff junction and loop problems

8. One loop, opposing sources

A 15 V and 3 V source oppose through 4 Ω and 2 Ω. Choose current in the 15 V source direction: 15−3−6I=0, so I=2 A. Drops 8 V and 4 V total 12 V, the net emf.

9. Junction reconstruction

At node P, 2.4 A and 1.1 A enter; I and 0.8 A leave. Charge conservation gives 3.5=I+0.8, so I=2.7 A leaving. If you assumed it entering, the solution would be −2.7 A.

10. Two-loop system

Two meshes share 2 Ω. Left source 10 V with outer 4 Ω; right source 4 V with outer 2 Ω. Choose clockwise mesh currents I₁ and I₂. Equations are 10−4I₁−2(I₁−I₂)=0 and 4−2I₂+2(I₁−I₂)=0. They simplify to 6I₁−2I₂=10 and −2I₁+4I₂=4, giving I₁=2.4 A and I₂=2.2 A. Shared current is 0.2 A in I₁’s direction.

Substitute into both original loops. Left: 10−9.6−0.4=0. Right: 4−4.4+0.4=0. The double check is part of the solution.

Round 5

Graphs, meters and investigation evaluation

11. V–I graph

A straight V-versus-I graph passes through (0.20 A, 2.4 V) and (0.60 A, 7.2 V). Gradient ΔV/ΔI=12 Ω. Because it passes through origin and keeps constant slope under stated conditions, the component is consistent with ohmic behaviour.

12. Meter loading

A 10 kΩ voltmeter across a 10 kΩ resistor makes their parallel equivalent 5 kΩ. The measurement can materially alter a high-resistance circuit. An “ideal” meter assumption should be stated, not silently transferred to every real setup.

Plan a low-voltage I–V investigation: independent variable is applied potential difference; dependent variable is current; control conductor, geometry and temperature. Place meters correctly, increase voltage in small steps, switch off between readings if heating matters, repeat and plot with units. Identify resolution, contact resistance and heating as limitations.

Practise safely with the PhET DC virtual lab. Never connect an ammeter directly across a source and never use household mains for this activity.

Round 6

Unworked challenge and marking framework

A wire’s length triples and diameter halves. Find the resistance factor.
Design 8 Ω using only identical 12 Ω resistors and explain the topology.
Reduce 3 Ω+(6 Ω∥(2 Ω+4 Ω)).
Across 18 V, recover every current, drop and power in that network.
A 1.5 V cell gives 1.2 V at 0.60 A. Find r and internal power.
Solve a two-loop circuit after reversing one source.
Draw correct meter placement for one branch current and one resistor voltage.
Explain a curved filament-lamp I–V graph.
Find total energy transferred by a 24 W load in 15 minutes.
Audit whether all source power is accounted for.

Award marks for diagram, governing equation, substitution, unit and check. For Kirchhoff work, also award current arrows and sign convention. For explanations, require a named conservation law or element model.

Use the OpenStax circuits exercise bank for further questions. After marking, create one isomorphic problem with changed values and one contrast problem with changed topology. Explain each correction aloud before consulting notes.

For online or physical NEB tuition, call 9846662070.

Frequently asked questions

Questions students ask about the DC circuits practice set

Should I combine resistors before using Kirchhoff rules?

Combine only clear series or parallel groups; otherwise use node and loop equations directly.

What checks catch most network errors?

Use equivalent-resistance bounds, branch-current sums, loop-voltage sums and total-power balance.

Is emf always equal to terminal voltage?

Only when current is negligible in the simple internal-resistance model; while supplying current V=ε−Ir.

Why do loop currents become negative?

The actual current direction is opposite to your chosen arrow; keep the equations and interpret the sign.

How should I mark a practical question?

Credit variables, circuit, meter ranges, safe procedure, repeated data, graph, uncertainty and limitations.

Where can I get worked-practice help?

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

References and next steps

Sources and related study guides

Revisit the concept guide after error analysis and use the study guide to schedule retests. Curriculum scope and linked institutional sources were checked on 2 August 2026; follow current CDC, NEB, school and laboratory instructions if requirements change.

Final transfer

One network, four controlled changes

Take the mixed-network example and repeat it after doubling the source voltage, opening one parallel branch, halving the series resistor and adding a small internal resistance. Before each calculation, state which node voltages, branch currents, equivalent resistance and powers should rise, fall or remain unchanged. After solving, compare the prediction with conservation checks.

This exercise distinguishes proportional reasoning from memorised formulas. For an ideal ohmic network, doubling source voltage doubles currents and quadruples resistor powers. Opening a parallel branch increases equivalent resistance and normally lowers source current. Adding internal resistance lowers terminal voltage under load and introduces internal power loss. A change in one branch can alter the voltage across other elements when a shared series resistor is present.

Write a short examiner-style marking scheme: topology, governing equations, substitution, units, bounds and interpretation. Then exchange only the circuit drawing style—not the node connections—and solve once more. If your answer changes, revisit node identification.

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