Alternating Current
Alternating current (AC) is current whose magnitude and direction vary sinusoidally with time. It is the form of electricity delivered by the power grid (in the US, 60 Hz, 120 V rms). For the MCAT, the essential ideas are the AC-vs-DC distinction, root-mean-square (rms) values, and the electromagnetic-wave spectrum — the detailed AC circuit analysis below is included only for completeness.
AC through Resistor, Capacitor and Inductor
An alternating EMF source delivers a sinusoidal voltage V = V0 sin(ωt), where V0 is the peak voltage and ω = 2πf is the angular frequency. The instantaneous current is I = I0 sin(ωt ± φ), where φ is the phase angle that depends on the circuit element.
Pure resistive circuit (R only)
Ohm's law applies at every instant: V = IR. Current and voltage are in phase (φ = 0). Both reach their peaks simultaneously and pass through zero together.
- Peak current: I0 = V0/R
- RMS values: Vrms = V0/√2, Irms = I0/√2
- Average power: P = Vrms Irms = Irms2 R
Capacitors and inductors in AC (survey level — low-yield)
The remaining points in this section are peripheral for the MCAT; skim them for context. A capacitor or inductor opposes AC through a frequency-dependent quantity called reactance (units Ω), and neither dissipates any average power — each merely stores and returns energy each cycle.
- Capacitor: capacitive reactance XC = 1/(2πfC) decreases as frequency rises, so a capacitor passes high-frequency AC but blocks DC (acts as an open circuit at DC).
- Inductor: inductive reactance XL = 2πfL increases with frequency, so an inductor passes DC freely but opposes high-frequency AC.
- Only the resistive part of a circuit dissipates real power (as heat); average power in a pure capacitor or pure inductor is zero.
Full quantitative treatment of series-RLC impedance, resonance, phasors, and power factor is beyond the AAMC outline and is omitted here.
Electromagnetic Waves Spectrum
An accelerating charge radiates an electromagnetic (EM) wave — a self-propagating disturbance of mutually perpendicular E and B fields, both perpendicular to the direction of travel. EM waves travel through vacuum at c ≈ 3 × 108 m s−1 and obey c = fλ.
Order of the spectrum (long λ → short λ)
- Radio waves
- λ > 1 m, f < 300 MHz. Used in broadcasting, communication, MRI. Generated by oscillating circuits and antennas.
- Microwaves
- λ ~ 1 mm to 1 m. Used in radar, microwave ovens (water rotation), satellite links, mobile phones.
- Infrared (IR)
- λ ~ 700 nm to 1 mm. Felt as heat. Emitted by all warm bodies; used in remote controls, thermal imaging.
- Visible light
- λ ~ 400 nm (violet) to 700 nm (red). The only band detected by the human eye.
- Ultraviolet (UV)
- λ ~ 10 nm to 400 nm. Causes sunburn and skin cancer; sterilises water and surfaces.
- X-rays
- λ ~ 0.01 nm to 10 nm. Penetrate soft tissue; used in radiography and crystallography.
- Gamma rays (γ)
- λ < 0.01 nm. Highest frequency, highest energy. Emitted by nuclear transitions and used in radiotherapy.
Phase of AC (survey level)
The phase of an AC quantity tells you where in the cycle the wave is; the phase difference between two quantities is the angular separation of their peaks. For the MCAT it is enough to know qualitatively that in a pure resistor current and voltage are in phase, while a capacitor or inductor introduces a 90° phase shift between them. Detailed phasor analysis and power factor (cosφ) are beyond the outline.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. US household mains is rated 120 V rms. Its peak voltage is approximately:
V0 = Vrms × √2 = 120 × 1.414 ≈ 170 V. RMS is the equivalent DC value that would dissipate the same average power; the peak is always √2 times higher for a sinusoid.
Q2. In a pure capacitive AC circuit, the current:
Remember ICE: in a Capacitor, I leads E by 90°. The capacitor charges fastest when voltage is changing fastest (at zero), and charge accumulates a quarter cycle later when voltage is at its peak.
Q3. A resistor carries a sinusoidal AC with peak current I0 = 2.0 A. The average power it dissipates equals that of a steady DC current of:
The heating (average power) of an AC is set by its rms value: Irms = I0/√2 = 2.0/1.414 ≈ 1.4 A. A 1.4 A DC would dissipate the same average power P = Irms2R. This is exactly why rms values are used.
Q4. Which electromagnetic wave has the longest wavelength?
Radio waves sit at the long-wavelength, low-frequency end of the EM spectrum (λ > 1 m). Gamma rays sit at the opposite end (λ < 0.01 nm). All EM waves travel at c in vacuum.
Q5. In a vacuum, how do the speeds of radio waves, visible light, and X-rays compare?
All electromagnetic waves travel at c ≈ 3 × 108 m/s in vacuum, regardless of frequency, and obey c = fλ. They differ in frequency and wavelength (and therefore photon energy E = hf), not in speed.
Quick Recap
- High-yield: Vrms = V0/√2, Irms = I0/√2; US mains 120 V rms → ~170 V peak.
- rms is the equivalent DC value; average power in a resistor P = Irms2R.
- EM spectrum order: Radio → Microwave → IR → Visible → UV → X-rays → Gamma; all travel at c in vacuum (c = fλ).
- Low-yield / off-outline (survey only): reactance XC = 1/(2πfC) and XL = 2πfL; capacitor blocks DC, inductor passes DC; reactive elements dissipate no average power; series-RLC impedance and resonance.