Circuits and Domestic Electricity
FoundationOhm's law V = IR underpins circuit calculations; series circuits share the current and parallel circuits share the voltage; power P = VI and bills are counted in kilowatt-hours; home wiring stays safe with live, neutral and earth wires plus fuses.
- I = Q/t; Ohm's law V = IR is the cornerstone of circuit calculations
- Series: same current, voltage shared by resistance, resistances added directly; parallel: same voltage, current divided inversely by resistance, reciprocals added
- Electrical power P = VI = I²R = V²/R; energy E = Pt
文體小知識：科學知識說明文——由歐姆定律講起，經串聯並聯計算走到家居用電與電費，把電學理論接上生活安全。
§Text Passage
1Modern life runs on electricity. Electric current is a directed flow of charge, its size equal to the charge passing through a cross-section per second; a source provides the voltage that drives the charges. A conductor's opposition to current is its resistance. The German scientist Ohm found that for a metallic conductor at constant temperature, the voltage across it is proportional to the current through it, and their ratio is the resistance — Ohm's law, the cornerstone of all circuit calculations.
2Circuits have two basic connections. In series, appliances are chained end to end: the current is the same everywhere, the total resistance is the sum of the resistances, and the voltage is shared in proportion to resistance. In parallel, appliances are connected across the same pair of nodes: every branch has the same voltage, the reciprocal of the total resistance equals the sum of the reciprocals, and current divides inversely with resistance. Home appliances are wired in parallel, so each can switch on and off independently at 220 V.
3As current passes through an appliance it does work, converting electrical energy into light, heat or kinetic energy. Electrical power measures how fast energy is used and equals voltage times current; combined with Ohm's law it can also be written as current squared times resistance, or voltage squared over resistance. The rated power printed on an appliance is its power when working normally at the rated voltage. Power multiplied by time gives the energy consumed — the basis of every electricity bill.
4The commercial unit of electrical energy is the kilowatt-hour, colloquially one 'degree' of electricity: a 1 kW appliance running for one hour uses 1 kW h, equal to 3.6 million joules. The power company charges by the degree, so choosing suitably rated appliances and switching off idle lights directly cuts the bill. For example, a 1500 W hairdryer used for two hours consumes 3 degrees; air conditioners are far more powerful, and leaving one on all day costs a lot — saving electricity starts with knowing power.
5Safety comes first in domestic wiring. The circuit has three wires: the live wire carries the high voltage, and the switch and fuse must be fitted in it; the neutral wire completes the loop; the earth wire connects the metal casing of an appliance to the ground, so that if a fault makes the casing live, current is led harmlessly to earth instead of through a person. Fuses and circuit breakers cut the circuit when the current is too large, preventing overheated cables from starting fires. The third pin of a three-pin plug is exactly this earth protection — never remove it or use a two-pin adapter for convenience.
1Summary 重點摘要
Ohm's law V = IR underpins circuit calculations; series circuits share the current and parallel circuits share the voltage; power P = VI and bills are counted in kilowatt-hours; home wiring stays safe with live, neutral and earth wires plus fuses.
2Vocabulary cards Vocabulary
A directed flow of charge, equal to the charge passing per second, I = Q/t, measured in amperes (A).
The energy converted per unit charge passing between two points, in volts (V); it drives the current.
A conductor's opposition to current, equal to voltage divided by current, in ohms (Ω).
For a metallic conductor at constant temperature, voltage is proportional to current: V = IR.
Components chained end to end: the current is common, R = R₁ + R₂ + …, and voltage divides in proportion to resistance.
Components connected across the same pair of nodes: the voltage is common, 1/R = 1/R₁ + 1/R₂, and current divides inversely with resistance.
The rate at which an appliance converts electrical energy: P = VI = I²R = V²/R, in watts (W).
The commercial unit of electrical energy: the energy used by a 1 kW appliance in one hour, 3.6 × 10⁶ J — one 'degree'.
A low-melting-point wire that melts and breaks the circuit when the current exceeds its rating; it must be fitted in the live wire.
The wire connecting an appliance's metal casing to the ground, carrying leakage current away to prevent electric shock.
3Step by step Steps
- Step 1: Current and Ohm's lawCurrent I equals the charge passing per second, I = Q/t, in amperes. Ohm's law states that for a metallic conductor at constant temperature, voltage is proportional to current, with the resistance R as the constant: V = IR. For example, a resistor connected to a 6 V supply carries 0.5 A, so its resistance is 6 ÷ 0.5 = 12 Ω; double the voltage to 12 V and the current doubles to 1 A. Circuit problems usually begin by identifying two known quantities and using Ohm's law to find the third — mastering this triangle is the foundation of every electricity calculation.
- Step 2: Series circuits — one current, shared voltageA series circuit offers a single path: the current is the same everywhere, each resistor shares the voltage in proportion to its resistance, and total resistance is the plain sum. For example, two 6 Ω resistors in series across a 12 V battery give 12 Ω total, a current of 1 A, and 6 V across each resistor; change the pair to 4 Ω and 8 Ω and the 8 Ω takes the larger share. Series appliances constrain each other: one burnt bulb in a string of Christmas lights blacks out the whole string — one reason homes are not wired in series.
- Step 3: Parallel circuits — one voltage, divided currentIn a parallel circuit every branch has the same voltage, the current divides inversely with resistance, and the reciprocal of the total resistance equals the sum of the reciprocals — always less than the smallest branch resistance. For example, two 6 Ω resistors in parallel give 3 Ω; add a third 6 Ω in parallel and the total falls to 2 Ω: more branches, lower total resistance, larger total current. Homes are wired in parallel so every appliance gets the full 220 V and switches independently — convenient, but the total current must not exceed the rating of the cables and fuse.
- Step 4: Three formulas for electrical powerElectrical power is voltage times current: P = VI; substituting Ohm's law gives P = I²R = V²/R. Each form has its moment: use VI when the current is known, I²R in series circuits (same current) and V²/R in parallel circuits (same voltage). For example, a 220 V, 60 W bulb draws I = 60 ÷ 220 ≈ 0.27 A, and its filament resistance is about 220² ÷ 60 ≈ 807 Ω. Picking the right form greatly simplifies the arithmetic — a favourite of multiple-choice questions, so practise until the choice is instinctive.
- Step 5: Electrical energy and the kilowatt-hourEnergy equals power times time: E = Pt. Commercially it is measured in kilowatt-hours: a 1 kW appliance for one hour uses 1 degree, equal to 3.6 × 10⁶ J. For example, a 2000 W fan heater running 3 hours uses 2 kW × 3 h = 6 degrees; at about $1.2 per degree that costs $7.2. To calculate a bill, convert watts to kilowatts first, multiply by hours to get degrees, then multiply by the tariff; never multiply the watt figure directly by hours and call it degrees. Misplacing the conversion loses the whole question — a classic careless error.
- Step 6: The three-wire household systemHousehold wiring has three wires: the live wire delivers the high voltage to appliances, the neutral wire completes the loop, and the earth wire connects the metal casing to the ground. The switch and fuse must sit in the live wire so that when the circuit is opened the appliance is no longer live, making inspection and repair safe. For example, a washing machine's metal case is earthed through the third pin of its plug: if an internal fault makes the case live, current flows harmlessly to earth instead of through anyone touching it; remove the earth and this defence fails completely. Distinguishing the colours and roles of the three wires is a common short question.
- Step 7: Choosing fuses and circuit breakersA fuse is a low-melting-point alloy wire that heats up and melts when the current exceeds its rating, breaking the circuit; a circuit breaker trips by electromagnetic or thermal action and can be reset. The rating must match the appliance: too small and it blows constantly, too large and it offers no protection. For example, a 2750 W water heater on a 220 V supply draws 12.5 A, so a 13 A fuse and suitably thick cable are appropriate; fitting a 5 A fuse by mistake means it blows at switch-on. Long questions often ask for the operating current from the power rating and then the fuse choice — both steps for full marks.
4Diagrams Diagrams
5Worked example Example
Example: (a) Two resistors of 4 Ω and 12 Ω are connected in parallel across a 6 V battery. Find the total resistance and the total current. (b) A hairdryer rated 1500 W is used 2 hours daily. With electricity at about $1.2 per kW h, find the total cost over 30 days.
- Parallel total resistance: 1/R = 14 + 112 = 312 + 112 = 412, so R = 3 Ω (necessarily less than the smaller 4 Ω)
- Total current: I = V/R = 6 ÷ 3 = 2 A
- Daily energy of the hairdryer: 1500 W = 1.5 kW; 1.5 × 2 = 3 kW h, i.e. 3 degrees per day
- Over 30 days: 3 × 30 = 90 degrees; cost = 90 × $1.2 = $108
- Answer: (a) Total resistance 3 Ω, total current 2 A. (b) The hairdryer uses 90 degrees in 30 days, costing $108. For parallel combinations add reciprocals; bills are counted in kilowatt-hours. In both parts, state the formula, substitute the numbers and give the units.
6Common mistakes Mistakes
7Quick check Quick check
Q1State Ohm's law and the units of each quantity.
Q2Two 6 Ω resistors in series: what is the total resistance? And in parallel?
Q3A heater runs on a 220 V supply with a current of 5 A. Find its power.
Q4A 1000 W heater runs for 3 hours. How many degrees of electricity does it use?
Q5Why must the fuse be fitted in the live wire?
8Recap Recap
- I = Q/t; Ohm's law V = IR is the cornerstone of circuit calculations
- Series: same current, voltage shared by resistance, resistances added directly; parallel: same voltage, current divided inversely by resistance, reciprocals added
- Electrical power P = VI = I²R = V²/R; energy E = Pt
- 1 kW h (one degree) = 3.6 × 10⁶ J; bills count degrees — convert to kilowatts first, then multiply by hours
- Domestic wiring uses live, neutral and earth wires; switch and fuse sit in the live wire, and the three-pin plug earths the metal casing against leakage