A-Level Physics May/June 2024 Q5(b)(ii): The electromotive force (e.m.f.) of the cell is 1.50 V. When the values of R₁ and R₂ ar…

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  First, calculate the total resistance $R_T$ of the parallel combination of $R_1$ and $R_2$.

  $R_T = \frac{R_1 \times R_2}{R_1 + R_2}$

  $R_T = \frac{10 \times 15}{10 + 15} = \frac{150}{25}$

  $R_T = 6.0 \, \Omega$

  Next, calculate the total current $I$ flowing from the cell using the potential difference $V$ across the parallel combination.

  $V = I R_T$

  $I = \frac{V}{R_T} = \frac{1.38}{6.0} = 0.23 \, \text{A}$

  Finally, use the e.m.f. equation including internal resistance $r$ to find the value of $r$. The potential difference across the terminals $V$ is the e.m.f. $E$ minus the 'lost volts' across the internal resistance.

  $E = V + Ir$

  $E - V = Ir$

  $r = \frac{E - V}{I}$

  $r = \frac{1.50 - 1.38}{0.23} = \frac{0.12}{0.23}$

  $r = 0.5217... \, \Omega$

  $r \approx 0.52 \, \Omega$ (to 2 s.f.)

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  How the marks are awarded

  • C1 — The first mark is for correctly calculating the total equivalent resistance of the two parallel resistors, which is 6.0 Ω.
  • C1 — The second mark is for stating a correct relationship for internal resistance, such as $r = (E-V)/I$, and correctly calculating the current $I$ (0.23 A) needed for this calculation.
  • A1 — The final mark is for the correct calculation of the internal resistance, resulting in an answer of 0.52 Ω.

  Common mistakes

  • Calculating the total external resistance by adding the resistors as if they were in series (10 + 15 = 25 Ω).
  • Using the e.m.f. (1.50 V) instead of the terminal p.d. (1.38 V) to calculate the current in the external circuit, i.e. calculating I = 1.50 / 6.0.
  • Incorrectly rearranging the e.m.f. equation, for example calculating r = V / I instead of r = (E-V) / I.
  • Making a calculation error when finding the parallel resistance, such as inverting the formula to (R₁+R₂)/(R₁R₂).

  Examiner tip: Always break down complex circuit problems into smaller, manageable steps, such as calculating total resistance first, then current, before finding the final unknown.

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