Kitchen Socket Overload, Warm Cable and a Faulty Iron
A family in a 1980s terrace house runs four appliances from one 13 A switched socket in the kitchen, using a three-way adapter: a 2.0 kW kettle, a 1.5 kW steam iron, a 0.60 kW rice cooker and a 0.10 kW refrigerator. The supply is 240 V. The socket circuit is protected by a 30 A miniature circuit breaker at the consumer unit, and the adapter's flexible cable is 8 m of 0.75 mm² copper wire that passes under a floor mat and feels warm after twenty minutes. The consumer unit also contains a 30 mA residual current device. One morning the heating element of the iron touches its metal soleplate; the iron still works normally. The user, standing on a dry tiled floor, receives a shock only when she touches the iron and the earthed metal sink at the same time.
1. Calculate the total current drawn with all four appliances running, and predict what happens to the 13 A fuse in the adapter plug and to the 30 A circuit breaker.
Read the worked answer
Total power: (P = 2000 + 1500 + 600 + 100 = 4200\text{ W})
Total current: (I = P/V = 4200/240 = 17.5\text{ A})
Fuse: 17.5 A exceeds the 13 A fuse rating by a large margin. A cartridge fuse is not instantaneous - it is a thermal device - but at roughly 1.35 times its rating it will melt within a few minutes, and at the kettle's 8.3 A alone plus the iron it is already close to the limit. The fuse therefore blows (or the plug's fuse ruptures) and cuts off all four appliances, which is correct behaviour: the fuse is protecting the adapter cable, not the appliances.
Circuit breaker: the 30 A MCB sees only 17.5 A, which is well below its rating, so it does not trip. This is important - the MCB protects the fixed wiring in the wall (rated ~30 A), while the 13 A fuse protects the flexible cord and adapter. Two devices in series protect two different parts of the installation, and one cannot substitute for the other.
Conclusion: running all four from one socket is a misuse; at least two should be moved to a separate circuit.
2. The 8 m, 0.75 mm² adapter cable becomes warm and is trapped under a mat. Explain the physics and quantify why this is dangerous, using the idea of voltage drop.
Read the worked answer
Why it warms. Copper has resistivity (\rho \approx 1.7\times10^{-8}\ \Omega\text{ m}). For the cable:
(R = \frac{\rho L}{A} = \frac{1.7\times10^{-8}\times16}{0.75\times10^{-6}} \approx 0.36\ \Omega)
(16 m because the current goes out and back.)
At 17.5 A the power dissipated in the cable itself is:
(P = I^2R = 17.5^2\times0.36 \approx 110\text{ W})
That is a heater inside a flexible cord - more than a typical light bulb - spread over a small surface area.
Voltage drop: (V = IR = 17.5\times0.36 \approx 6.3\text{ V}), so the appliances receive only about 234 V. Motor loads such as the refrigerator draw a larger current at reduced voltage, adding to the total and worsening the heating.
Why the mat matters. Heat loss by convection and radiation is blocked, so the equilibrium temperature of the insulation rises far above what it would be in open air. PVC insulation softens and can carbonise; carbonised insulation becomes conductive and can track, causing a fire even before any fuse operates.
Correct practice: use a shorter, thicker cable (1.5 mm² minimum for a 13 A extension), never coil or cover it, and avoid adapters. The 13 A fuse limits current but does not prevent a 110 W dissipation in a poorly chosen cord.
3. Explain why the iron is still working normally yet gives a shock only when the user also touches the sink, and discuss whether the 30 mA RCD will protect her.
Read the worked answer
Why it still works. The element touches the soleplate but the element itself is intact and still connected live-to-neutral, so the heating current and the appliance's operation are unaffected. The fault is a leakage path from live metal to the earthed casing, not a break in the circuit.
Why only with the sink. Touching the iron alone does not complete a circuit - she stands on dry tiles, which are a poor conductor, so essentially no current flows and there is no shock. When she touches the earthed metal sink at the same time, she completes a path: live casing → her body → sink → earth. Her body resistance, perhaps 1–5 kΩ for dry skin but falling rapidly once current flows, limits the current, and a few tens of milliamps through the chest can cause ventricular fibrillation.
Role of the RCD. The 30 mA RCD monitors the difference between live and neutral currents. When she touches the sink, the imbalance equals the current through her body. If that exceeds 30 mA, the RCD trips within about 30 ms and limits the duration of the shock. It does not protect against a live-to-neutral shock (no imbalance, so no trip), and it does not operate before she touches the sink, because before that there is no earth path at all.
The missing protection is the earth wire. The iron's metal casing should be earthed through the third pin. With a sound earth, the fault current would flow casing → earth conductor → back to the supply, blowing the 13 A fuse immediately and disconnecting the iron before anyone touches it. The shock therefore indicates a broken or missing earth connection (or a two-pin adapter defeating it), which is the primary defect to repair.