A-Level Physics May/June 2024 Q7(b)(v): The variation of V with t can be described by V = A sin Bt where A and B are constants.…

1 answer

• ▲0
  accepted ✓

  By comparing the given equation $V = A \sin(Bt)$ with the standard equation for a sinusoidal alternating voltage, $V = V_0 \sin(\omega t)$:

  The constant $A$ is the amplitude or peak voltage, $V_0$. From part (b)(iii), the peak e.m.f. is 0.82 V. $A = 0.82 \text{ V}$

  The constant $B$ is the angular frequency, $\omega$. The relationship between angular frequency and the period $T$ is $\omega = \frac{2\pi}{T}$. From the previous part of the question, the period $T = 2.0 \times 10^{-3} \text{ s}$.

  $B = \frac{2\pi}{2.0 \times 10^{-3}}$ $B = 3141.59... \text{ rad s}^{-1}$ $B \approx 3100 \text{ rad s}^{-1}$ (to 2 s.f.)

  $A = 0.82 \text{ V}$ $B = 3100 \text{ rad s}^{-1}$

  ---

  How the marks are awarded

  • A1 — The value for the amplitude A is correctly identified as the peak voltage, 0.82 V (or the value from (b)(iii)), and is stated with the correct unit 'V'.
  • C1 — The correct formula for the angular frequency B, $B = 2\pi / T$, is used with the correct substitution for the period, $T = 2.0 \times 10^{-3}$ s.
  • A1 — The value for B is calculated correctly to be 3100 (or 3140) and is given with the correct unit, rad s⁻¹.

  Common mistakes

  • Calculating frequency $f = 1/T$ for B instead of angular frequency $\omega = 2\pi/T$.
  • Forgetting to include units for A and B, or using incorrect units such as Hz for B.
  • Using an incorrect value for the period T, for example by misreading a graph or forgetting to convert milliseconds to seconds.
  • Confusing peak voltage (for A) with r.m.s. voltage, and calculating $A = V_{peak} / \sqrt{2}$.

  Examiner tip: Always compare the given equation to its standard physical form (in this case, $V = V_0 \sin(\omega t)$) to directly identify the physical meaning of the constants.

  ---

  AI-generated model answer, grounded in the official Cambridge mark scheme and reviewed by the MarkScheme team. Mark your own answer to this question →

  @markscheme_answers

Your answer

Sign in to answer this question.