Current Electricity - Quick Revision
Current and Ohm's law
- Electric current I = q/t is the net charge crossing a cross-section per unit time (a scalar). SI unit: ampere.
- Ohm's law: V = IR, where R (ohm) is resistance. Ohm's law is not fundamental; it fails for diodes, GaAs, etc.
- Resistance R = rho L/A. Resistivity rho is a material property: metals ~10^-8 to 10^-6 ohm m, insulators ~10^18 times higher, semiconductors in between.
Drift and resistivity
- Free electrons drift opposite to E with drift velocity vd = eE tau/m; current I = nAe vd; current density j = I/A = sigma E.
- rho = m/(n e^2 tau). Mobility mu = vd/E = e tau/m.
Combinations
- Series: Rs = R1 + R2 + ... (same current). Parallel: 1/Rp = 1/R1 + 1/R2 + ... (same voltage).
Cells, emf, internal resistance
- emf = open-circuit terminal voltage. With current: V = emf - Ir; I = emf/(R + r); Imax = emf/r.
- Series (aiding): emf_eq = e1 + e2, r_eq = r1 + r2. Parallel: 1/r_eq = 1/r1 + 1/r2.
Power, Kirchhoff, Wheatstone
- Power: P = VI = I^2 R = V^2/R. Transmission loss minimized at high V (Pc = P^2 Rc/V^2).
- Kirchhoff: junction rule (charge conservation, sum in = sum out); loop rule (energy, sum of potential changes = 0).
- Wheatstone bridge balanced when R2/R1 = R4/R3 (null deflection).