6.4 Properties of Electrical Materials & Engineering Sciences
Key Takeaways
- Resistance R = rho·L/A, where rho is resistivity (ohm·m); conductors have low rho, insulators have very high rho, and semiconductors lie between with conductivity that rises with temperature and doping.
- Conductor resistance increases with temperature: R(T) = R0·[1 + alpha·(T - T0)], where alpha is the temperature coefficient of resistance.
- A capacitor's capacitance scales with the dielectric's permittivity: C = epsilon·A/d = epsilon_r·epsilon_0·A/d, so higher relative permittivity stores more charge per volt.
- Charge, current, and power link by Q = I·t and P = V·I; energy W = P·t = V·I·t, with electrical energy often billed in kilowatt-hours.
- Engineering Sciences on the FE EE/CE blends work-energy-power, basic statics/dynamics, and thermal/charge fundamentals shared with other engineering disciplines.
Why materials and engineering sciences matter
Two distinct NCEES knowledge areas meet here. Properties of Electrical Materials (about 4 to 6 questions) asks how materials conduct, insulate, store charge, and respond to magnetic fields. Engineering Sciences (about 6 to 9 questions) is the shared foundation across FE disciplines: work, energy, power, basic statics and dynamics, and thermal and charge fundamentals. These questions are usually short and definitional, so they are efficient points if you know the relations and units.
Conductors, semiconductors, and insulators
Materials are classified by how easily they carry current, quantified by resistivity rho (ohm·meter) or its inverse, conductivity sigma:
- Conductors (copper, aluminum): very low rho, many free electrons; resistivity rises with temperature.
- Semiconductors (silicon, germanium): intermediate rho; conductivity increases with temperature and with doping, which is the basis of diodes and transistors.
- Insulators / dielectrics (glass, rubber, polymers): very high rho; resist current flow and support electric fields.
Resistance of a uniform sample is R = rho·L/A, where L is length and A is cross-sectional area. Longer or thinner samples have higher resistance.
Temperature, dielectrics, and magnetic materials
Conductor resistance changes with temperature:
R(T) = R0·[1 + alpha·(T - T0)]
where alpha is the temperature coefficient of resistance (positive for metals). This is why motor windings read higher resistance when hot.
Dielectric behavior governs capacitors. Capacitance is C = epsilon·A/d = epsilon_r·epsilon_0·A/d, where epsilon_0 = 8.854e-12 F/m is the permittivity of free space and epsilon_r is the relative permittivity (dielectric constant). A higher dielectric constant stores more charge per volt, while the dielectric strength sets the maximum field before breakdown.
Magnetic materials are classified as diamagnetic, paramagnetic, or ferromagnetic (iron, steel) with high relative permeability used in transformer and motor cores, where hysteresis and eddy currents cause core losses.
Work, energy, power, and charge fundamentals
Engineering Sciences links mechanical and electrical quantities through energy.
| Quantity | Relation | SI unit |
|---|---|---|
| Charge | Q = I·t | coulomb (C) |
| Electrical power | P = V·I = I^2·R = V^2/R | watt (W) |
| Energy | W = P·t | joule (J) or kWh |
| Mechanical work | W = F·d | joule (J) |
| Kinetic energy | KE = (1/2)·m·v^2 | joule (J) |
A watt is one joule per second, so power is the rate of energy transfer. Electrical energy is often billed in kilowatt-hours (1 kWh = 3.6e6 J). Thermal energy uses Q = m·c·deltaT, where c is specific heat. Keeping units coherent (joules, watts, seconds, or their USCS equivalents) prevents most Engineering Sciences errors.
A copper wire has resistance 5 ohms. A second copper wire of the same material has twice the length and half the cross-sectional area. What is its resistance?
Which material category has electrical conductivity that increases as temperature rises and can be tailored by doping?
A device draws 2 A at 120 V for 3 hours. How much electrical energy does it consume?