Chapter 3: Electricity

3.1 Current and Potential Difference

• An electric field is the region around a charged particle where any electric charge experiences an electric force. (p.94)
• Field lines point outward from positive charges and inward to negative charges; they never cross. (p.94)
• Electric field strength: E = F/q (unit N C⁻¹). (p.95)
• Between parallel plates: E = V/d (unit V m⁻¹); the field is uniform. (p.95)
• A charged metal-coated polystyrene ball swings between two charged plates. (p.97)
• Current is the rate of flow of charge: I = Q/t. (p.98)
• Potential difference is the work done to move one coulomb of charge between two points: V = W/Q. (p.99)
• Charge of an electron e = 1.6 × 10⁻¹⁹ C; 1 C = 6.25 × 10¹⁸ electrons. (p.99)

3.2 Resistance

• Ohm's law: V is directly proportional to I at constant temperature; V = IR. (p.100)
• Ohmic conductor: straight-line V–I graph through the origin, constant resistance. Non-ohmic conductor: curved graph, resistance increases. (p.102)
• Series: I same; V = V₁ + V₂ + V₃; R = R₁ + R₂ + R₃. (p.103)
• Parallel: V same; I = I₁ + I₂ + I₃; 1/R = 1/R₁ + 1/R₂ + 1/R₃. (p.103)
• Resistance increases with length, decreases with cross-sectional area; higher resistivity gives higher resistance. (p.108)
• R = ρl/A; the unit of resistivity is ohm-metre (Ω m). (p.110)
• Heating elements need high resistivity and high melting point; connecting wires use copper because of its low resistivity. (p.111)
• Superconductors have zero resistivity at or below the critical temperature, T_c. (p.112)

3.3 Electromotive Force (e.m.f.) and Internal Resistance

• e.m.f. is the energy transferred or work done by an electrical source to move one coulomb of charge in a complete circuit: ε = E/Q. (p.114)
• e.m.f. is the voltmeter reading in an open circuit; the closed-circuit reading is the potential difference. (p.116)
• Internal resistance, r, is the resistance caused by the electrolyte in the cell; it causes voltage drop Ir = ε − V. (p.117)
• ε = V + Ir = I(R + r); the graph of V against I has gradient −r and V-intercept ε. (p.118)
• Cells in series: higher total e.m.f., r_e = nr. Cells in parallel: lower effective internal resistance, r_e = r/n. (p.120)

3.4 Electrical Energy and Power

• Electrical energy: E = VIt. (p.124)
• Electrical power: P = E/t = VI = I²R = V²/R (unit W or J s⁻¹). (p.125)
• Energy cost = units (kWh) × cost per unit; 1 kWh = 1 unit. (p.127)
• Saving electricity: switch off unused appliances, use energy-saving lamps, use full washing loads. (p.128)