Electric Potential, Potential Energy & Capacitors — Practice · Grade 12 Science

Chapter: Electricity, Magnetism & Circuits

What this practice covers

By the end of Electric Potential, Potential Energy & Capacitors you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: electric potential, capacitance, equipotential.

Problem 1

Charge 3C moves through a +4 V difference. Find ΔU.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

12 J

qΔV=12.

Problem 2

How do potential and field differ?
Answer and explanation

Potential is scalar energy per charge; field is vector force per charge.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

Find capacitor charge at C=.004 F and V=3 V.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

0.012 C

Q=CV=.012.

Problem 4

Why is capacitor energy not always QV?
Answer and explanation

Voltage grows during charging; average charging voltage is half final voltage for a linear capacitor.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

A capacitor has C=4.0×10⁻⁶ F at 10 V. Find stored charge. Show the reasoning, not just the conclusion.
Hints

Potential is per charge; energy change also depends on q.

Answer and explanation

Q=CV=4.0×10⁻⁵ C on either plate in magnitude.

Problem 6

Find energy for that capacitor using U=½CV².
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

½×4.0×10⁻⁶×100=2.0×10⁻⁴ J.

Problem 7

Capacitance relates separated charge to potential differenceCapacitance relates separated charge to potential difference+−+−+−Parallel-plate capacitor: charge separation stores energyC=Q/V; Q is magnitude on either plate, not total net charge.
Original ideal parallel-plate model; fringing fields and material details are omitted.
Interpret the supplied visual. For C=20 μF and V=12 V, what is plate charge magnitude?
Answer and explanation

Q=CV=240 μC, with equal opposite signs on the two ideal plates.

A capacitor stores energy through separated opposite charges. Its capacitance C=Q/V uses the magnitude Q on either plate and the plate-to-plate potential difference, under a linear model. The entire ideal two-plate device can have zero net charge while each plate is charged. Farads are coulombs per volt. Geometry and dielectric material affect capacitance; doubling Q at fixed C doubles V rather than necessarily changing C itself.

Q=CV=240 μC, with equal opposite signs on the two ideal plates.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

A 50 μF capacitor is at 8 V. Find Q and U; compare U at 16 V in the same ideal model.
Answer and explanation

Q=400 μC; U=½×50×10⁻⁶×64=0.0016 J=1.6 mJ. At16 V, U=6.4 mJ, four times as much. Actual ratings must be separately respected.

Q=400 μC; U=½×50×10⁻⁶×64=0.0016 J=1.6 mJ.

At16 V, U=6.4 mJ, four times as much.

Actual ratings must be separately respected.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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