One Circuit, Four Loads, and a 32 A Breaker
A first-floor rented room in Phnom Penh is supplied from a single 16 A miniature circuit breaker (MCB) in the landlord's board. The cable is 2.5 mm² copper, run 25 m from the board to the room's sockets (copper resistivity 1.7 × 10⁻⁸ Ω·m); the supply is 230 V, 50 Hz. On the circuit are an air conditioner drawing 1.50 kW, an electric kettle rated 1.80 kW, and four LED lamps of 20 W each. The landlord says a 16 A breaker is 'plenty' because 16 × 230 = 3680 W, which covers everything. He now wants to add a 2.00 kW instant water heater to the same circuit, and to swap the 16 A MCB for a 32 A one so that it will not trip. The kettle has a metal body and its socket has two pins only, with no earth connection. The tenant also reports that the LED lamps dim every time the kettle switches on.
1. Calculate the circuit current with and without the water heater. Evaluate the landlord's 3680 W argument and his plan to fit a 32 A breaker.
Read the worked answer
Without the heater: P = 1500 + 1800 + 4(20) = 3380 W, so I = 3380/230 = 14.7 A. With the heater: P = 5380 W, I = 23.4 A.
The landlord's arithmetic is right but his reasoning is wrong in two ways. First, 14.7 A is already 92% of a 16 A breaker; good design keeps continuous loads at about 80% of the rating (≈12.8 A), so the existing circuit is marginal even before anything is added. Second, a breaker protects the cable, not the appliances. A 32 A breaker will happily pass 23–30 A through a 2.5 mm² cable whose capacity in conduit or insulation is roughly 18–24 A depending on how it is run. The cable then overheats inside the wall while the breaker stays closed.
Verdict: do not fit the 32 A MCB. The water heater needs a dedicated circuit - 4 mm² cable and its own breaker sized to that cable - or the heater should not be installed. Adding load and enlarging the protective device at the same time removes both safety layers at once.
2. Estimate the voltage drop to the room at the present load, and use it to judge whether the cable explains the dimming lamps.
Read the worked answer
The current travels out and back, so the cable length is 2 × 25 = 50 m.
R = ρL/A = (1.7 × 10⁻⁸ × 50) / (2.5 × 10⁻⁶) = 3.4 × 10⁻¹ Ω = 0.34 Ω ΔV = I × R = 14.7 × 0.34 ≈ 5.0 V 5.0/230 = 2.2%
A 2.2% drop is within normal installation limits (typically 3–5%), and it is far too small to make LED lamps visibly dim. LEDs tolerate a few percent of supply variation without noticeable change, since their drivers regulate output over a wide input range. So the cable resistance is not the explanation.
The correct judgement is to challenge the symptom's assumed cause. A step change in brightness when a 1.8 kW load switches on points to a bad connection - a loose terminal screw, a corroded or back-stabbed socket, an overloaded shared neutral - giving a resistance far larger than 0.34 Ω and a local hot spot. That is a fire risk, not a nuisance, and should be inspected before any new load is added. Dimming at the instant of switching can also come from the kettle's own arcing, but that would not persist.
3. Explain to the landlord, in physical terms, why the unearthed metal kettle is the most urgent problem in the room.
Read the worked answer
With a two-pin socket the kettle's metal body has no deliberate path to earth. If a fault develops - a damaged element sheath, a chafed internal wire touching the casing, or water ingress - the body sits at 230 V while the kettle continues to work normally. Nothing trips, because the fault current has no return path; the circuit behaves as though it were healthy.
The hazard appears only when a person touches the casing while also in contact with earth (a damp floor, a tap, a concrete wall). Then the person becomes the return path: at 230 V and a body resistance of roughly 1–2 kΩ under wet conditions, the current is of the order of 100–200 mA, well above the 30 mA threshold at which muscle contraction prevents letting go and ventricular fibrillation becomes likely. A 16 A MCB will not respond to that current at all.
The fix is a three-pin socket with a proper protective earth, backed by a 30 mA RCBO, plus routine checks of the kettle's flex and plug. In a rented room where rewiring may be slow, a plug-in 30 mA RCD unit at the socket is a reasonable interim measure, and the kettle should be replaced with a double-insulated model if earthing cannot be provided.