A student connects three identical resistors, each of resistance 6 Ω, first in series and then in parallel across the same 12 V battery.
(i) Calculate the equivalent resistance and total current drawn from the battery in each case.
(ii) Using your calculated values, find the ratio of currents drawn in the parallel and series combinations. Explain, in terms of how equivalent resistance changes with configuration, why such a large difference in current arises.
(iii) In a household, electrical appliances are connected in parallel rather than in series. Using your findings above, give TWO distinct reasons why parallel connection is preferred.
Generated by claude-sonnet-4-6 · 2026-06-26 01:11 · grounding rag
Model Answer
(i) Series combination:
$R_s = 6 + 6 + 6 = 18\ \Omega$
$I_s = V/R_s = 12/18 = 0.67\ \text{A}$
Parallel combination:
$\frac{1}{R_p} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6}$, so $R_p = 2\ \Omega$
$I_p = V/R_p = 12/2 = 6\ \text{A}$
(ii) Ratio of currents:
$$\frac{I_p}{I_s} = \frac{6}{0.67} = 9:1$$
In series, equivalent resistance increases (equals sum of all resistances = 18 Ω). In parallel, equivalent resistance decreases below the smallest individual resistance (= 2 Ω). Since $I = V/R$ and voltage is the same, the 9-fold lower resistance in parallel draws 9 times more current.
(iii) Two reasons parallel connection is preferred in households:
- Each appliance gets the full supply voltage (220 V), so every device operates at its rated capacity independently.
- If one appliance fails, the others continue to work, since each is on a separate branch — unlike series, where one failure breaks the entire circuit.
Source: Chapter 11, Sections 11.6.1 and 11.6.2
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Explanation
- For part (i), always show the formula, substitution, and unit — examiners award step marks.
- For part (ii), the ratio $I_p : I_s = 9 : 1$ directly follows from $R_s/R_p = 18/2 = 9$; state this link clearly.
- For part (iii), the textbook explicitly lists these two advantages in Section 11.6.2 — use those exact points. Do not invent new ones.
- Keep calculations neat; a missing unit can cost half a mark.