Electrical Systems – Quick Revision

Electric Circuits

• Circuit components: cell, battery, switch, lamp, fixed resistor, rheostat, ammeter, voltmeter

• Closed circuit → continuous conducting path; open circuit → no charge flow

• Short circuit = alternative path of $0\,\Omega$; all current bypasses load

• Series vs parallel wiring

  • Series: one path, same current, fault opens entire circuit

  • Parallel: multiple paths, current splits, other branches work if one fails

• Basic symbols must be used when drawing diagrams

Electric Current

• Definition: rate of flow of charge $I=\dfrac{Q}{t}$

• Unit: ampere (A); $1\,\mathrm{A}=1\,\mathrm{C\,s^{-1}}$

• Conventional current: $+ \rightarrow -$ terminal; electron flow opposite

• Ammeter: connect in series, red to $+$, black to $-$

Electromotive Force & Potential Difference

• e.m.f. (source): work done per unit charge round complete circuit

• p.d. (component): work done per unit charge across two points

• Both measured in volts (V)

• Relationships

  $\varepsilon<em>{\text{total}}=\varepsilon</em>1+\varepsilon_2+\cdots$

  • Voltmeters: connect in parallel with component

Resistance

• Definition: $R=\dfrac{V}{I}$ (ohm, $\Omega$)

• Fixed vs variable (rheostat) resistors

• Effective resistance

  • Series: $R<em>{\text{eq}}=R</em>1+R<em>2+R</em>3+\cdots$

  • Parallel: $\dfrac{1}{R<em>{\text{eq}}}=\dfrac{1}{R</em>1}+\dfrac{1}{R<em>2}+\dfrac{1}{R</em>3}+\cdots$

• Adding resistors: increases $R_{\text{eq}}$ in series, decreases in parallel

DC Circuit Rules

• Series circuit

  • Current: $I<em>1=I</em>2=I_3$

  • Voltage: $V<em>{\varepsilon}=V</em>1+V<em>2+V</em>3$

• Parallel circuit (two branches)

  • Current: $I=I<em>1+I</em>2$

  • Voltage: $V<em>{\varepsilon}=V</em>1=V_2$ (if purely parallel)

Electrical Power & Energy

• Power: $P=\dfrac{W}{t}=\dfrac{E}{t}$ (watt, W)

• Energy: $E=P\,t$ ; household unit $1\,\text{kWh}=3.6\times10^6\,\text{J}$

• Cost: $\text{Cost}=E_{(\text{kWh})}\times \text{rate}$

Dangers of Electricity

• Hazards: damaged insulation, overheating cables (overload/inadequate wire), damp conditions → shock or fire

Safety Features

• Fuse: thin wire in live line, melts when $I$ exceeds rating

• Circuit breaker: resettable switch trips at high $I$ (live line)

• Earthing: low-resistance path; large fault current blows fuse, keeps casing at $0\,\text{V}$

• Double insulation: no earth wire; plastic casing + internal insulation

• Switch position: always on live conductor

• Three-pin plug wiring

  • Live (brown) to fuse & switch

  • Neutral (blue) returns at $0\,\text{V}$

  • Earth (green/yellow) to metal casing