A 220 V electric iron rated 1000 W and a 220 V electric bulb rated 100 W are connected in parallel across a 220 V supply. (i) Calculate the resistance of each device. (ii) Calculate the total current drawn from the supply. (iii) If both devices are instead connected in series across the same 220 V supply, calculate the current through the circuit and explain why this series arrangement is unsuitable for practical household use, giving at least two distinct reasons.
Generated by claude-sonnet-4-6 · 2026-06-26 01:13 · grounding rag
Model Answer
(i) Resistance of each device:
Using $R = V^2/P$:
- Electric iron: $R_1 = \dfrac{(220)^2}{1000} = \dfrac{48400}{1000} = **48.4 \text{ Ω}**$
- Electric bulb: $R_2 = \dfrac{(220)^2}{100} = \dfrac{48400}{100} = **484 \text{ Ω}**$
(ii) Total current in parallel:
Current through iron: $I_1 = \dfrac{220}{48.4} \approx 4.55 \text{ A}$
Current through bulb: $I_2 = \dfrac{220}{484} \approx 0.45 \text{ A}$
Total current $I = I_1 + I_2 = 4.55 + 0.45 = **5 \text{ A}**$
(iii) Series connection:
Total resistance $R_s = 48.4 + 484 = 532.4 \text{ Ω}$
Current $I = \dfrac{220}{532.4} \approx **0.41 \text{ A}**$
Why series is unsuitable:
- Both devices share the same small current (≈0.41 A), but the iron needs ~4.55 A and the bulb ~0.45 A to work properly — neither device operates at its rated power.
- If one device fails/fuses, the circuit breaks and the other stops working too.
Source: Chapter 11 — Electricity, Sections 11.6.1 and 11.6.2
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Explanation
- The formula $R = V^2/P$ is the quickest route here since rated voltage and power are given directly.
- For part (ii), you can also use $I = P/V$ for each device — same result, equally accepted.
- In part (iii), the series current calculation must come first, then the two distinct reasons. Examiners award marks separately for the calculation and each reason, so state both reasons clearly. The textbook explicitly states that different gadgets need different currents and that series circuits fail completely when one component breaks — use these points.
- Do not confuse "unsuitable because voltage is divided" (that is a consequence) with the key reasons above; stick to what the textbook states.