Summary and Quick Revision

Current, charge, potential difference

  • Electric current = rate of flow of charge: I=QtI = \dfrac{Q}{t}; SI unit ampere (A), 1 A=1 C/s1\ \text{A} = 1\ \text{C/s}.
  • Conventional current is opposite to electron flow.
  • Potential difference V=WQV = \dfrac{W}{Q}; SI unit volt (V), 1 V=1 J/C1\ \text{V} = 1\ \text{J/C}.
  • Ammeter → series; Voltmeter → parallel.

Ohm's law and resistance

  • Ohm's law: V=IRV = IR (at constant temperature); VV-II graph is a straight line through the origin, slope = RR.
  • Resistance R=VIR = \dfrac{V}{I}; SI unit ohm (Ω).
  • R=ρlAR = \rho\dfrac{l}{A}: R ∝ length, R ∝ 1/area; ρ\rho = resistivity (Ω m), a material property.

Series vs Parallel

Series Parallel
Current same through each splits: I=I1+I2+…I = I_1+I_2+\dots
Voltage adds: V=V1+V2+…V = V_1+V_2+\dots same across each
Equivalent R Rs=R1+R2+…R_s = R_1+R_2+\dots (largest) 1Rp=1R1+1R2+…\dfrac{1}{R_p} = \dfrac{1}{R_1}+\dfrac{1}{R_2}+\dots (smallest)
  • Two in parallel: Rp=R1R2R1+R2R_p = \dfrac{R_1R_2}{R_1+R_2}.
  • Home wiring is parallel - each device gets full voltage and others keep working if one fails.

Heating effect, power and energy

  • Joule's law: H=I2RtH = I^2Rt (also H=VItH = VIt). Heat ∝ I2I^2, ∝ RR, ∝ tt.
  • Electric power: P=VI=I2R=V2RP = VI = I^2R = \dfrac{V^2}{R}; SI unit watt (W), 1 kW=1000 W1\ \text{kW} = 1000\ \text{W}.
  • Energy = power × time; commercial unit kilowatt-hour: 1 kW h=3.6×106 J1\ \text{kW h} = 3.6 \times 10^6\ \text{J}.
  • Fuse: thin low-melting-point wire in series; melts and breaks the circuit if current is too high.
  • Tungsten → bulb filament (high m.p.); alloys (nichrome) → heating elements; copper/aluminium → transmission lines.

Cost of energy = (power in kW) × (time in h) × (rate per unit). Because H∝I2H \propto I^2, doubling current gives 4× heat.