OCR · A-Level · Physics

    Course version: H556 · Version from Sept 2015

    (a) p.d. – charge graph for a capacitor; energy stored is area under graph

    Full specification wording

    Energy: (a) p.d. – charge graph for a capacitor; energy stored is area under graph

    For a capacitor, the p.d.

    Checked against the OCR H556 specification (opens in a new tab) on .

    • Point 1 of 3
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    For a capacitor, the p.d. V across it is proportional to the charge Q stored, so a graph of V against Q is a straight line through the origin with gradient 1/C. The energy stored is the work done in transferring charge against the increasing p.d., which equals the area under the V–Q graph. Because the graph is a triangle of base Q and height V, the area is ½QV. This geometric interpretation links directly to the energy formulae and explains why the factor ½ appears. A concrete check: if Q = 4.0 × 10⁻³ C and V = 20 V, the area is ½ × 4.0 × 10⁻³ × 20 = 4.0 × 10⁻² J.

    What earns the marks

    • State that p.d. is directly proportional to charge for a capacitor, giving a straight-line V–Q graph through the origin.
    • Explain that the energy stored equals the area under the p.d.–charge graph.
    • Calculate energy from the triangular area as ½QV.
    • Relate the gradient of the V–Q graph to 1/C.

    Common mistakes and how to put them right

    • Treating the V–Q graph as a rectangle and using QV without the factor ½.

      Put it right: The area is a triangle, so energy is ½QV.

    • Thinking the graph curves.

      Put it right: For an ideal capacitor V is proportional to Q, so the graph is straight.

    • Confusing the area under a V–Q graph with the area under a V–I graph.

      Put it right: They represent different quantities.

    Exam tips

    • Sketch the V–Q line and shade the triangular area to show where ½QV comes from.
    • Use the gradient to find 1/C and hence C if the graph is given.
    • Keep charge in coulombs and p.d. in volts so the area is in joules.

    Try the lesson

    The start of the Energy: (a) p.d. – charge graph for a capacitor; energy stored is area under graph lesson, made from checked teaching notes for this specification point.

    Listen

    For a capacitor, the p.d. V across it is proportional to the charge Q stored, so a graph of V against Q is a straight line through the origin with gradient 1/C. The energy stored is the work done in transferring charge against the increasing p.d., which equals the area under the V–Q graph. Because the graph is a triangle of base Q and height V, the area is ½QV. This geometric interpretation links directly to the energy formulae and explains why the factor ½ appears. A concrete check: if Q = 4.0 × 10⁻³ C and V = 20 V, the area is ½ × 4.0 × 10⁻³ × 20 = 4.0 × 10⁻² J. A strong answer earns marks for these points. State that p.d. is directly proportional to charge for a capacitor, giving a straight-line V–Q graph through the origin. Explain that the energy stored equals the area under the p.d.–charge graph. Calculate energy from the triangular area as ½QV. Relate the gradient of the V–Q graph to 1/C. Exam tip: Sketch the V–Q line and shade the triangular area to show where ½QV comes from.

    See it

    A top-down flowchart. The first box states that p.d. V is proportional to charge Q. An arrow leads to a box saying the V–Q graph is a straight line through the origin. From that box two arrows branch out: one to a box saying the gradient of the line is 1/C, and one to a box saying the energy stored equals the area under the V–Q graph. The area box leads to a box saying the area is a triangle with base Q and height V, which leads to a final box saying energy = ½QV.
    It shows how the straight-line V–Q graph through the origin leads to the gradient being 1/C and to the energy stored being the triangular area ½QV.

    Key words

    Say what each word means before you turn the card.

    Proportionality of charge and p.d.

    Try answering aloud or in your head before turning the card.

    Graphical representation of energy

    Try answering aloud or in your head before turning the card.

    Area under a graph as work done

    Try answering aloud or in your head before turning the card.

    Capacitance from gradient

    Try answering aloud or in your head before turning the card.

    See every definition
    Proportionality of charge and p.d.
    For a capacitor, the p.d. V across it is proportional to the charge Q stored, so a graph of V against Q is a straight line through the origin.
    Graphical representation of energy
    The energy stored is the work done in transferring charge against the increasing p.d., which equals the area under the V–Q graph.
    Area under a graph as work done
    Because the graph is a triangle of base Q and height V, the area is ½QV, which links directly to the energy formulae and explains why the factor ½ appears.
    Capacitance from gradient
    A graph of V against Q is a straight line through the origin with gradient 1/C.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The first box states that p.d. V is proportional to charge Q. An arrow leads to a box saying the V–Q graph is a straight line through the origin. From that box two arrows branch out: one to a box saying the gradient of the line is 1/C, and one to a box saying the energy stored equals the area under the V–Q graph. The area box leads to a box saying the area is a triangle with base Q and height V, which leads to a final box saying energy = ½QV.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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