An electric lamp (100 Ω), a toaster (50 Ω), and a water filter (500 Ω) are connected in parallel to a 220 V source. A fourth appliance — an electric iron — is then connected in parallel to the same source and draws the same total current as all three original appliances combined. Calculate the resistance of the electric iron.
Generated by claude-sonnet-4-6 · 2026-06-26 01:11 · grounding rag
Model Answer
Step 1: Find total current drawn by the three appliances (in parallel, V = 220 V)
$$I_1 = \frac{220}{100} = 2.2 \text{ A}, \quad I_2 = \frac{220}{50} = 4.4 \text{ A}, \quad I_3 = \frac{220}{500} = 0.44 \text{ A}$$
$$I_{total} = 2.2 + 4.4 + 0.44 = 7.04 \text{ A}$$
Step 2: The electric iron draws the same current = 7.04 A
Step 3: Resistance of electric iron
$$R_{iron} = \frac{V}{I} = \frac{220}{7.04} \approx 31.25 \text{ Ω}$$
The resistance of the electric iron is approximately 31.25 Ω.
Source: Chapter 11 (Electricity), Section 11.6 – Resistance of a System of Resistors
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Explanation
- In a parallel circuit, each appliance has the full 220 V across it, so use $I = V/R$ separately for each.
- Add all three currents to get the total; the iron draws this same total current.
- Apply Ohm's law ($R = V/I$) to find the iron's resistance.
- Examiners award marks for: correct individual currents (1 mark), correct total current (1 mark), and correct resistance of iron (1 mark). Show each step clearly.