Alternating Current: MDCAT Notes and MCQs
AC basics
- V = V0 sin ωt, ω = 2πf. Pakistan mains: 50 Hz, 220 V (rms).
- Phase: angle θ = ωt that specifies the instantaneous value and direction of an alternating quantity. Phase difference between V and I tells whether current leads or lags.
- Vrms = V0/√2 = 0.707 V0; Irms = I0/√2. Peak value of 220 V mains ≈ 311 V. Average over a full cycle = 0.
AC through components
| Element | Opposition | Phase | Power |
|---|---|---|---|
| Resistor | R (independent of f) | V and I in phase | Dissipated: P = VrmsIrms |
| Capacitor | XC = 1/(2πfC) — decreases with f (blocks DC) | Current leads voltage by 90° | Zero average |
| Inductor | XL = 2πfL — increases with f (passes DC) | Current lags voltage by 90° | Zero average |
Mnemonic "CIVIL": in a Capacitor I leads V; V leads I in an inductor (L). Impedance of RLC: Z = √(R² + (XL − XC)²); resonance when XL = XC: fr = 1/(2π√(LC)).
Electromagnetic spectrum
All EM waves travel at c = 3 × 108 m/s in vacuum, are transverse, carry energy and need no medium. In order of increasing frequency / decreasing wavelength:
| Wave | Approx. λ | Uses |
|---|---|---|
| Radio waves | > 0.1 m | Broadcasting, communication, MRI |
| Microwaves | 1 mm – 10 cm | Radar, mobile phones, microwave ovens |
| Infrared | 700 nm – 1 mm | Remote controls, thermal imaging, physiotherapy |
| Visible light | 400–700 nm | Vision, optical fibres (endoscopy) |
| Ultraviolet | 10–400 nm | Sterilization, vitamin D, fluorescence |
| X-rays | 0.01–10 nm | Radiography, CT scans, crystallography |
| Gamma rays | < 0.01 nm | Cancer therapy, sterilizing instruments |
PMDC learning outcomes for this unit
- AC & EM spectrum: 12.1 Describe the phase of alternating current and explain how phase lag and phase lead occur in AC circuits
- AC & EM spectrum: 12.2 Explain the flow of AC through resistors, capacitors and inductors
- AC & EM spectrum: 12.3 Become familiar with the EM spectrum (ranging from radio waves to gamma rays)