Dangers of electricity

Electric shock is current through the body, not just contact with voltage. The human body conducts electricity because it contains water and dissolved ions, and its resistance — mostly at the skin — normally limits how much current flows for a given voltage. Ohm's law, $I = V/R$, says the same thing about a body as about any conductor: for a fixed household voltage, a lower body resistance $R$ lets a larger current $I$ flow. Wet skin has far lower resistance than dry skin, since water provides an easy path for ions to carry charge, so the same touch on a live wire delivers a much larger, more dangerous current when hands or feet are wet. This is why bathrooms, wet floors and damp hands are flagged as high-risk situations even though the household voltage itself has not changed.

Fire is current turning into heat faster than it can escape. Any current flowing through a wire's resistance generates heat (the heating effect of current). A properly rated wire is designed so that this heat is dissipated safely at the current the circuit is meant to carry. Two faults push the heat past that safe limit:

• Short circuit — the live and neutral wires (or a live wire and an earthed metal part) touch directly, collapsing the circuit's resistance and causing a very large, sudden surge of current.
• Overloading — too many high-power appliances drawn from one socket or extension board push the current well above its rated value, generating steady excess heat over time.

Either fault can heat wiring enough to melt insulation and ignite nearby material.

where: $P$ is the heat generated per second (in watts), $I$ is the current flowing through the wire (in amperes), and $R$ is the wire's resistance (in ohms). The physical reading is the important part for this topic: heat grows with the square of the current, so even a moderate rise in current — from mildly overloading a socket — produces a much larger rise in heat than the same fractional rise in resistance ever could.

Two lines of defence. A fuse is a thin wire of low melting point placed in the circuit; when current exceeds its rated value, the fuse itself heats up fastest (being the weakest link) and melts, breaking the circuit before wiring elsewhere can overheat. Earthing connects an appliance's metal casing, via a low-resistance wire, to the ground; if a fault makes the casing live, fault current flows harmlessly to earth instead of through a person who touches the casing, and a large enough fault current will also blow the fuse.

Overloading is deceptively easy to underestimate because the extra current often looks small — one more appliance, not obviously "too much." But the heat generated in a wire depends on current squared, not on current directly, and that single fact is why a modest overload can produce a disproportionately large amount of heat, turning a survivable slip into a genuine fire hazard.

Step 1. Start from the heating relation $P = I^2R$ for a wire of fixed resistance $R$ carrying its rated safe current $I_1$. The steady heat generated per second is $P_1 = I_1^2R$, and the wire and its insulation are designed to safely dissipate exactly this much heat without overheating.

Step 2. Now suppose overloading raises the current to $I_2 = 1.5\,I_1$ — a fairly ordinary situation, such as running one extra appliance from the same socket. The new heat generated per second is $P_2 = I_2^2R = (1.5\,I_1)^2R = 2.25\,I_1^2R = 2.25\,P_1$.

Step 3. Compare the two: the current rose by a factor of $1.5$ (a 50% increase), but the heat generated rose by a factor of $2.25$ (a 125% increase). This squared relationship is the reason overloading feels harmless in the moment yet builds heat much faster than intuition suggests, since the wire's insulation was never designed to shed heat at more than twice the safe rate.

Step 4. If nothing intervenes, this extra heat keeps building because it is generated continuously while the overload persists, eventually softening or melting the wire's insulation and creating a fire risk near any flammable material nearby. A correctly rated fuse breaks the circuit once current crosses its threshold, stopping the heat build-up at $P_1$ before it can reach the dangerous $P_2$ level — which is exactly why a fuse must be rated close to, not far above, the circuit's safe current.

Question: A circuit is rated to carry a safe current of $5\ \text{A}$ through wiring of resistance $0.8\ \Omega$. A user plugs in extra appliances so the current rises to $8\ \text{A}$. Find the heat generated per second at the rated current and at the overloaded current, and state by what factor the heat has increased.

Step 1. Heat generated per second at the rated current: $P_1 = I_1^2R = (5)^2 \times 0.8 = 25 \times 0.8 = 20\ \text{W}$.

Step 2. Heat generated per second at the overloaded current: $P_2 = I_2^2R = (8)^2 \times 0.8 = 64 \times 0.8 = 51.2\ \text{W}$.

Step 3. Factor of increase: $P_2 / P_1 = 51.2 / 20 = 2.56$, while the current itself only rose by a factor of $8/5 = 1.6$. The heat generated per second rises from 20 W to 51.2 W — a 2.56-times increase from a current only 1.6 times larger — which is why this circuit's fuse must be rated at or just above 5 A to cut off the supply before the wiring reaches the dangerous 51.2 W level.

• Assuming shock danger depends only on the voltage present — it actually depends on the current that flows through the body, and wet skin lets far more current flow at the same voltage by lowering the body's resistance.
• Treating a small overload as harmless because the extra current "isn't much more" — since heat scales with current squared, a 50% rise in current can mean a 125% rise in generated heat.
• Believing fuses or earthing make careless behaviour safe on their own — these components limit the damage from a fault but do not replace dry hands, undamaged wiring and sensible loading of sockets.
• Overlooking a short circuit as just "a fire risk" without recognising it also drives an enormous, sudden current — exactly the kind of surge a correctly rated fuse is meant to interrupt immediately.

Ask the tutor: Want to work through a few more "what could go wrong here" household wiring scenarios, including how to size a fuse correctly for a given set of appliances?