Thermal effect of current and safety

One device works normally, but after several are connected the same wire becomes hot. Why does current affect the released energy more strongly than a simple doubling might suggest?

The field does work on moving charges; they interact with the conductor's material and transfer energy to it. In a resistive section, electrical energy becomes internal energy: this is Joule heating. The released energy Q is measured in joules. It may stay in the conductor or leave for the surroundings. A heating element can therefore keep releasing energy even after its temperature stops rising.

A resistor converts electrical power UI into heating. Substitute U = IR: over time t, the Joule–Lenz law gives Q = I²Rt for constant I and R. Units А²·Ом·с give joules. The square arises because increasing current at the same R also requires more voltage. At zero current, Joule heating is zero; twice the time gives twice the energy. Q is energy, not a number of degrees.

Double the current in one wire while keeping resistance and time unchanged. The formula contains (2I)² = 4I², so four times the energy is released. Increasing the load on shared wiring can therefore quickly increase heating. Keep comparison conditions clear: at fixed current, greater R gives more Q; at fixed voltage, current changes and Q = U²t/R. Resistances cannot be compared without stating what the source maintains.

Does four times Q mean four times the temperature? No: there is an initial temperature, and its change depends on mass and heat capacity. For an ideal thermally insulated conductor without a phase change, ΔT = Q/(cm). Real wire also transfers energy to air and supports. Temperature can become constant when release balances losses. If R changes during heating, one constant R cannot be used over the whole interval either.

A short circuit creates an unintended very low-resistance path between circuit points at different potentials, for example bypassing a load. Total current rises sharply; real resistance in the source, contacts and wires prevents it from becoming infinite. These parts release energy and may overheat. Low resistance in the shorting path therefore does not mean no dangerous heating elsewhere: the current has changed greatly.

A fuse or circuit breaker is selected to suit the wiring's current rating. Excess current makes it open the circuit, limiting the duration of energy release and reducing overheating risk. But a current dangerous to a person may be below its trip threshold. A normal breaker therefore mainly protects wiring; it does not guarantee protection when someone touches a live part. Never change its rating yourself just to stop it tripping.

Damaged insulation may allow current to pass through a person; wet hands often lower contact resistance. Do not touch bare wires or damaged devices, or handle electrical appliances with wet hands. If you find damage, stop using the device and tell an adult. School experiments use a purpose-designed low-voltage source and a checked circuit. Understanding heating explains the rules; it does not make dangerous contact an acceptable experiment.

Protection has different roles. Insulation prevents contact with a conductor. Protective earthing provides an intended fault-current path and helps disconnection after a fault. A residual-current device detects a difference between outgoing and returning currents, which may indicate leakage. These measures reduce particular risks, but do not permit touching live parts. Specialists check their condition and correct use.

A constant 2 A flows through a 5 ohm resistor for 60 s. Find the energy released.

We need the resistor's released energy; current and resistance are constant. Use Q = I²Rt.

The current is squared: 2² = 4. Thus Q = 4·5·60 = 1200 Дж. The release rate is 20 W; over 60 s this gives the same 1200 J.

This is not a temperature answer. For temperature, we need mass, heat capacity, initial temperature and energy exchange with the surroundings.

1200 J. Each second, 20 J was released; some may have transferred to surrounding objects.

Q = I²Rt explains quadratic growth in released energy as current rises with R and t unchanged.

Temperature also depends on energy accumulation and removal; a short circuit changes current throughout the real circuit.

Different protective devices serve different purposes; touching live parts remains unacceptable.

Current not only heats a conductor: it creates a magnetic field. We will study its effects next.