Domestic installations and supplies

Match each component of a dwelling's consumer unit with its function: (1) power limiter (ICP), (2) main circuit breaker (IGA), (3) residual current device (RCD) and (4) miniature circuit breakers (MCBs) for each circuit, with: (a) cuts off the supply if you exceed the contracted power; (b) allows the power to the entire dwelling to be cut off at once and protects the whole installation against overcurrents; (c) protects people against earth leaks or current leakages; (d) protects the wiring of each circuit against overloads and short circuits.

Explain the two hazards that a miniature circuit breaker (MCB) protects against in each circuit: overload (too many appliances running at once, which heats up the cables gradually) and a short circuit (direct contact between live and neutral, causing a sudden, massive current).

The figure shows the single-line diagram of a dwelling's consumer unit, with an element marked with a question mark, as shown in the figure.

(a) Identify the element marked with the question mark and explain its protective function. (b) Describe the order of the components in the consumer unit and reason why the RCD is placed before the MCBs of each circuit. (c) Explain what happens in each case: an MCB trips, the RCD trips, or the power limiter trips, and how to reset them.

A dwelling has a contracted power of $4{,}6\ \text{kW}$. In the kitchen, the oven ($3\ \text{kW}$) and the hob ($2\ \text{kW}$) are operating simultaneously. (a) Calculate the total power and reason what happens to the power limiter. (b) Propose two ways to solve the problem without changing electricity supplier: a management solution (not using both at the same time) and a technical solution (increasing the contracted power), commenting on what each implies for the electricity bill.

In a home with a single-phase supply at $230\ \text{V}$ and a contracted power of $5{,}75\ \text{kW}$ (limited to $25\ \text{A}$), the main distribution board has four circuits: C1 lighting ($10\ \text{A}$, $1{,}5\ \text{mm}^2$ cable), C2 general-purpose sockets ($16\ \text{A}$, $2{,}5\ \text{mm}^2$ cable), C3 cooktop and oven ($25\ \text{A}$, $6\ \text{mm}^2$ cable), and C4 washing machine and water heater ($20\ \text{A}$, $4\ \text{mm}^2$ cable). A user observes that the sum of the ratings of the four miniature circuit breakers (MCBs) is $71\ \text{A}$ and claims: "The installation is oversized and poorly designed; furthermore, to prevent the power from tripping when I simultaneously turn on a $2.000\ \text{W}$ radiator in the living room, the $2.800\ \text{W}$ oven, and the $1.500\ \text{W}$ water heater, I will replace the $16\ \text{A}$ MCB with a $25\ \text{A}$ one."\n\n(a) Refute the first part of the statement by technically justifying why the sum of the rated currents of the MCBs can be three times that of the main switch (ICP), referring to the concepts of diversity factor (simultaneity) and protection selectivity.\n(b) Calculate the total current that the three appliances would demand operating at the same time and quantitatively determine which switch in the chain will cut off the supply and under what physical principle (thermal or magnetic).\n(c) Justify the real risks of fire and deterioration if the $16\ \text{A}$ MCB of C2 were replaced with a $25\ \text{A}$ one without changing the $2{,}5\ \text{mm}^2$ wiring (whose allowable current-carrying capacity $I_z$ in conduit embedded in a wall is about $18\ \text{A}$).

The figure shows the consumer unit (distribution board) of a home with the ratings of its protection devices, with the maximum power of one of the circuits marked with a question mark.

(a) In a home appliance connected to circuit C2, an insulation fault occurs whereby the live conductor touches the metal casing through a contact resistance $R_{\text{def}} = 4.600\ \Omega$. Knowing that the building's earth connection has $R_{\text{tierra}} = 20\ \Omega$, calculate the earth leakage current and determine with reasoned arguments whether the RCD in the diagram will trip or not.\n(b) If an induction hob and an oven demanding a combined $6.440\ \text{W}$ are simultaneously used in circuit C3, determine which device (the main limiter ICP or the MCB of C3) will trip first if in the rest of the house only $230\ \text{W}$ of lighting in C1 is turned on.\n(c) Explain why the residual current device (RCD) has a rated current of $40\ \text{A}$ marked on it when the upstream limiter is $25\ \text{A}$, and what thermal danger would exist if that RCD were rated at only $16\ \text{A}$ in the event of an overall overload.

Describe the path of the water supply in a dwelling: where it enters (main stopcock and water meter), what two internal distribution networks exist (cold water and hot water downstream of the water heater) and which device should be checked to prevent leaks.

Gas can be supplied via mains (mains natural gas) or bottled (butane or propane cylinder). Explain one advantage of each supply method and two essential safety measures in a gas kitchen (permanent ventilation and inspection of hoses and valves).

A family evaluates whether to replace their traditional butane gas cooker with an electric induction hob. To prepare their monthly meals, they need to transfer a net useful thermal energy of $100\ \text{kW}\cdot\text{h}$ to the cookware.\n\nTechnical and economic data:\n- Gas cooker: supplied by $12{,}5\ \text{kg}$ butane cylinders ($LCV = 12{,}8\ \text{kW}\cdot\text{h}/\text{kg}$). Due to thermal losses from convection and radiation to the environment, the efficiency of the gas burner is only $42\,\%$. The price of a cylinder is $17{,}50\ \text{€}$.\n- Induction hob: directly heats the ferromagnetic base of the vessel, with an overall energy efficiency of $84\,\%$. The cost of the electricity consumed is $0{,}19\ \text{€}$ per $\text{kW}\cdot\text{h}$.\n\n(a) Calculate the gross primary energy contained in a full cylinder and determine how many cylinders per month (or fraction of a cylinder) the family needs with the gas cooker.\n(b) Calculate the monthly electricity consumption in billed $\text{kW}\cdot\text{h}$ needed to provide exactly the same $100\ \text{kW}\cdot\text{h}$ of useful heat with the induction hob.\n(c) Determine the monthly cost of fuel/electricity for both alternatives and justify why comparing only the price per gross $\text{kW}\cdot\text{h}$ of gas versus electricity leads to an erroneous conclusion.\n(d) Analyse what impact the installation of the induction hob (typical maximum power of $7\ \text{kW}$) could have on the contracted electrical power of the home and the fixed term of the bill.

Describe the components of telecommunications in a dwelling: what comes in from the street (fibre optic or cable), what the router does (distributes the connection via Ethernet cable and Wi-Fi) and why the router's position has such a major impact on wireless coverage.

In a two-story home with a reinforced concrete structure, a user has a $600\ \text{Mbps}$ symmetric fiber connection. The main router is located on the ground floor. In the upper-floor office, a room dedicated to critical remote work, the WiFi coverage in the $5\ \text{GHz}$ band drops to $-85\ \text{dBm}$ (with frequent disconnections), and in the $2{,}4\ \text{GHz}$ band it barely achieves $15\ \text{Mbps}$ with an average latency of $95\ \text{ms}$. The home electrical panel has independent circuits for both floors, each protected by a different residual current device (RCD).\n\n(a) The user purchases a "$1.000\ \text{Mbps}$" PLC (Powerline) kit and a standard plug-in WiFi repeater. Physically justify why both solutions will fail to deliver a high-speed, low-latency connection in this specific scenario (analyze the high-frequency filtering introduced by RCDs and coils in the electrical grid for the PLC, and the bandwidth loss due to half-duplex operation and floor slab attenuation in the WiFi repeater).\n(b) To install a network cable to the upper floor, running an Ethernet cable through the same corrugated conduits carrying the $230\ \text{V}$ phase, neutral, and ground wires is considered. Explain what electromagnetic induction issues (crosstalk/noise) and what regulatory impediments according to the REBT arise, and what type of shielded cable (FTP/STP) or physical alternative (such as plastic optical fiber, POF) would solve the problem safely.\n(c) Design the ideal network topology for this home, detailing the necessary components (router, switch, wired access point), the configuration of radio channels and bands to avoid overlap, and how to configure the identifier (SSID) to enable seamless roaming without connection drops.