Current Electricity, Ohm's Law and Energy Cost

What you need to know

• Electric current is the rate of flow of charge, I = Q/t, measured in amperes. One coulomb is the charge that passes when a current of one ampere flows for one second. Conventional current flows from positive to negative, opposite to the actual drift of electrons.
• Potential difference between two points is the work done in moving one coulomb of charge between them, V = W/Q, measured in volts. Electromotive force is the total energy supplied by a source per coulomb, including the energy wasted inside the source itself.
• Ohm's law states that the current through a conductor is directly proportional to the potential difference across its ends, provided temperature and other physical conditions remain constant. Hence V = IR, and R is the resistance in ohms.
• A conductor obeying Ohm's law gives a straight-line V against I graph through the origin, and the slope of that line is the resistance. A filament lamp, a thermistor and a diode are non-ohmic, so their graphs are curved.
• Resistance of a uniform wire R = rho L / A: it increases with length, decreases with cross-sectional area, and depends on the resistivity of the material. For most metals resistance rises with temperature; for semiconductors and thermistors it falls.
• Resistors in series carry the same current and their resistances add: R = R1 + R2 + R3. The potential difference divides between them in proportion to their resistances.
• Resistors in parallel have the same potential difference across each and their reciprocals add: 1/R = 1/R1 + 1/R2. The combined resistance of a parallel arrangement is always smaller than the smallest individual resistor, and for just two resistors R = R1R2/(R1 + R2).
• A real cell has internal resistance r, so E = I(R + r) and the terminal potential difference V = E - Ir. The terminal p.d. falls as the current drawn rises, which is why car headlamps dim briefly when the starter motor is engaged.
• Cells in series give E(total) = sum of the emfs and r(total) = sum of the internal resistances, which is used when a large voltage is wanted. Identical cells in parallel keep the emf of one cell but reduce the internal resistance to r/n, which is used when a large current is wanted.
• Electrical energy W = IVt = I^2Rt = V^2t/R, in joules, and electrical power P = IV = I^2R = V^2/R, in watts. A device rated 240 V, 1000 W draws I = P/V = 1000/240 = 4.17 A.
• The commercial unit of electrical energy is the kilowatt-hour, the energy used by a 1 kW appliance running for 1 hour. One kWh = 1000 W x 3600 s = 3.6 x 10^6 J. The energy meter in a house counts kilowatt-hours, and the bill is kWh used multiplied by the tariff per kWh.
• The ammeter is connected in series and should have very low resistance; the voltmeter is connected in parallel across the component and should have very high resistance. Connecting an ammeter in parallel across a supply short-circuits it and can destroy the meter.
• A fuse is a thin wire of low melting point placed in the live wire; it melts and breaks the circuit when the current exceeds its rating. A fuse is rated slightly above the normal working current of the appliance. Earthing carries fault current safely to ground, and switches must always be fitted in the live wire.
• A primary cell such as the Leclanche or dry cell cannot be recharged, while a secondary cell such as the lead-acid accumulator or a lithium-ion battery stores charge chemically and can be recharged. Defects of the simple voltaic cell are polarisation, cured by a depolariser such as manganese dioxide, and local action, cured by amalgamating the zinc with mercury.