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PhysicsDifficulty 1-4

Electricity

Electricity is the behaviour of electric charge, and an electric current is charge flowing round a complete circuit, measured in amperes. A battery's potential difference (voltage) pushes the current, resistance opposes it, and for many materials they are linked by Ohm's law, V = IR. Circuits transfer energy at a rate P = IV; resistors add in series and combine as reciprocals in parallel. Mains electricity can kill and is never used for experiments.

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Charge Flow in Conductors

Instantaneous current is I = dQ/dt. The SI defines the ampere through the exactly fixed elementary charge e = 1.602176634 × 10⁻¹⁹ C, so 1 A corresponds to 1/e ≈ 6.24 × 10¹⁸ elementary charges per second.

I=dQdt,I=nqAvdI = \dfrac{dQ}{dt}, \qquad I = nqAv_d

Current as rate of charge flow, and in terms of carrier density n, carrier charge q, cross-sectional area A and drift speed (v with subscript d).

Because n is very large in a metal, the drift speed is only of order 10⁻⁴ m/s, while the electrical signal propagates at of order 10⁸ m/s: the field and the mutual repulsion of charges transmit the push along the wire almost at once. Electrons carry negative charge, so they drift opposite to conventional current.

For networks, series and parallel rules are special cases of Kirchhoff's rules: the junction rule (charge conservation — current in equals current out) and the loop rule (potential changes around a closed loop sum to zero), giving Rₛ = ΣRᵢ and Rₚ = (Σ 1/Rᵢ)⁻¹. The power delivered by the source equals the total power dissipated in the resistors.

Warning: Shock severity depends mainly on the current through the body, together with its path, the shock's duration and its frequency. Wet skin can lower body resistance enough that the same voltage drives a dangerous current, and the UK HSE warns that contact above about 50 V AC can cause a range of injuries, including problems with breathing and heart function.
Full explanation — the complete reference version every reading depth is based on
Warning: Safety first: mains electricity (the sockets in your home and anything plugged into them) can kill. Never experiment with sockets, plugs, chargers or appliances, never touch electrical things with wet hands, and never connect a battery's terminals directly together — a short-circuited battery can overheat or burst. Hands-on electricity activities should only ever use low-voltage battery kits, with an adult.

Charge and current

Everything is built from atoms containing positive and negative electric charge. Charge is conserved: it can move about, but the net charge of a closed system never changes. An electric current is a flow of charge, and it only flows when there is a complete path — a circuit — from one terminal of the source, through the device and back to the other.

I=ΔQΔt,1 A=1 C/sI = \dfrac{\Delta Q}{\Delta t}, \qquad 1\ \text{A} = 1\ \text{C/s}

Current is the rate of flow of charge; one ampere is one coulomb per second.

  • The SI defines the ampere by fixing the elementary charge at exactly 1.602176634 × 10⁻¹⁹ C, so 1 A means about 6.24 × 10¹⁸ elementary charges passing each second (1 ÷ 1.602176634 × 10⁻¹⁹, our calculation).
  • Conventional current is drawn from + to −, the way positive charge would move; in metal wires the electrons actually drift the other way.
  • The electrons themselves drift slowly — around 10⁻⁴ m/s — yet a lamp lights almost instantly because each charge pushes the next, so the signal travels at around 10⁸ m/s.

Voltage, resistance and Ohm's law

A battery provides a potential difference called its emf (electromotive force — a historical name, since it is not a force). The potential difference drives current; resistance, measured in ohms (Ω), opposes it. Georg Simon Ohm first showed experimentally that the current in a metal wire is proportional to the voltage across it.

V=IRV = IR

Ohm's law: voltage (V) equals current (A) times resistance (Ω), for ohmic materials.

P=IV=I2R=V2RP = IV = I^2R = \dfrac{V^2}{R}

Electrical power (W) transferred in a resistor.

Series and parallel

  • Series: one path. The same current passes through every component, the supply voltage is shared between them, and resistances simply add. If one lamp in a series string fails, the whole string goes dark.
  • Parallel: separate branches. Each branch gets the full supply voltage, the branch currents add up to the total, and the combined resistance is less than the smallest single resistance.
RS=R1+R2+…R_S = R_1 + R_2 + \dots

Equivalent resistance of resistors in series.

1RP=1R1+1R2+…\dfrac{1}{R_P} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots

Equivalent resistance of resistors in parallel.

Worked example: a 9 V circuit

A 9 V supply drives 100 Ω and 220 Ω resistors in series — the default of the ScienceVerse electric-circuits simulation. Total resistance R = 100 + 220 = 320 Ω, so I = V/R = 9/320 ≈ 0.0281 A (28.1 mA). The voltage divides in proportion to resistance: 0.028125 A × 100 Ω ≈ 2.81 V and 0.028125 A × 220 Ω ≈ 6.19 V, which add back to 9 V. Total power P = IV ≈ 0.253 W. Rewire the same two resistors in parallel and Rₚ = 1/(1/100 + 1/220) ≈ 68.8 Ω, so the battery supplies about 0.131 A — more than either branch would draw alone. These are exactly the numbers the simulation shows (28.125 mA in series), because it uses the same equations.

Why it can be dangerous

A shock happens when current passes through a person. Its effects range from a slight tingle or pain to loss of muscle control, difficulty breathing, an irregular heartbeat and death; the size of the current through the body is a major factor, along with the path it takes, how long it lasts and its frequency. The UK Health and Safety Executive notes that contact with more than about 50 V AC can cause a range of injuries, including problems with breathing and heart function. Water makes things worse: in a textbook example a soaking-wet person's resistance is about a twentieth of the same person's when dry (10 kΩ against 200 kΩ), so the same voltage drives about twenty times the current. Body resistance is never predictable, and mains electricity is never safe to touch, wet or dry.

Common misconception: Misconception: a lamp 'uses up' current, so less current leaves it than enters. Charge is conserved, so in a series circuit the same current flows all the way round. What the lamp takes is energy, which it transfers to light and heat.
Common misconception: Misconception: electrons race round the circuit at nearly the speed of light. The electrons drift very slowly; it is the push passed from charge to charge along the wire that travels fast.
Info: Assumptions and limits: Ohm's law is an empirical relationship — an observed pattern, like friction — not a fundamental law. Many components, such as diodes, are non-ohmic: their current is not proportional to voltage. The worked example and the circuits simulation also assume an ideal battery with no internal resistance, wires with no resistance, and resistors that do not change as they warm up.

Where electricity connects

Electricity draws on Forces (charges push and pull) and Energy (circuits transfer it at a rate P = IV). Moving charges produce magnetic fields — the doorway to Magnetism — and the heating of resistors links it to Thermodynamics.

How we know

These relationships come from measurement. Georg Simon Ohm was the first to show experimentally that the current in a metal wire is proportional to the voltage across it. Volta's voltaic pile, the first battery, gave experimenters a steady source of current. Today an ammeter placed in series measures current and a voltmeter placed in parallel measures potential difference, so anyone with a safe low-voltage kit can check that series currents are equal and that branch currents in parallel add up to the total.

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Content status: published 1 October 2026.

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