Alternating Current
Alternating current (AC) is current whose magnitude and direction vary sinusoidally with time. It is the form of electricity delivered by Pakistan's national grid (50 Hz, 220 V rms). The PMDC MDCAT 2026 syllabus expects you to handle AC through pure R, C and L circuits, the electromagnetic wave spectrum, and the concept of phase. This chapter typically delivers 1-2 MCQs.
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
Pure capacitive circuit (C only)
The capacitor opposes a change in voltage. Current leads voltage by 90° (φ = −90°). The opposition to AC is called capacitive reactance.
- XC = 1 / (2πfC) = 1 / (ωC), measured in Ω
- I0 = V0 / XC
- XC ↓ as f ↑ — capacitor "passes" high frequencies, blocks DC.
- Average power dissipated = 0 (purely reactive).
Pure inductive circuit (L only)
The inductor opposes a change in current via a back-EMF. Current lags voltage by 90° (φ = +90°). The opposition is called inductive reactance.
- XL = 2πfL = ωL
- I0 = V0 / XL
- XL ↑ as f ↑ — inductor blocks high frequencies, passes DC freely.
- Average power dissipated = 0.
| Property | Pure resistor (R) | Pure capacitor (C) | Pure inductor (L) |
|---|---|---|---|
| Opposition (Ω) | R (resistance) | XC = 1/(ωC) = 1/(2πfC) | XL = ωL = 2πfL |
| Phase angle φ (V vs I) | 0° (in phase) | −90° — current leads voltage | +90° — current lags voltage |
| Effect of frequency ↑ | No change | XC ↓ (passes high f, blocks DC) | XL ↑ (blocks high f, passes DC) |
| Behaves at DC | Acts as resistor | Open circuit (XC → ∞) | Short circuit (XL → 0) |
| Average power dissipated | P = Irms2R (heat) | 0 (energy stored / returned) | 0 (energy stored / returned) |
| Energy stored as | None (dissipated) | Electric field | Magnetic field |
In a series RLC circuit the total opposition to AC is the impedance Z = √(R2 + (XL − XC)2). The phase angle is tanφ = (XL − XC) / R. Resonance occurs when XL = XC, giving Z = R (minimum) and fr = 1 / (2π√(LC)).
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
The phase of an AC quantity is the argument of its sine function and tells you where in the cycle the wave is. The phase difference φ between two quantities is the angular separation of their peaks.
- Pure R
- I and V are in phase (φ = 0). Both peak together.
- Pure C
- I leads V by π/2 rad (90°). Mnemonic: ICE — in a capacitor, I comes before E (voltage).
- Pure L
- I lags V by π/2 rad. Mnemonic: ELI — in an inductor, E (voltage) comes before I.
Power factor
The factor cosφ in P = VrmsIrmscosφ is the power factor. It equals 1 for a pure resistor (all power dissipated) and 0 for a pure inductor or capacitor (no real power dissipated). Industrial loads strive for cosφ close to 1 to minimise wasted apparent power.
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. The peak value of an alternating voltage of 220 V rms is approximately:
V0 = Vrms × √2 = 220 × 1.414 ≈ 311 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. The reactance of a 100 µF capacitor at 50 Hz is closest to:
XC = 1/(2πfC) = 1/(2π × 50 × 100 × 10−6) = 1/(0.0314) ≈ 31.8 Ω. Capacitive reactance is inversely proportional to both frequency and capacitance.
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. The condition for resonance in a series RLC circuit is:
At resonance the inductive and capacitive reactances cancel, leaving only R. Impedance is minimum, current is maximum, and the resonant frequency is fr = 1/(2π√(LC)).
Quick Recap
- I = I0 sin(ωt), V = V0 sin(ωt); ω = 2πf.
- Vrms = V0/√2, Irms = I0/√2; mains 220 V rms → 311 V peak.
- Pure R: φ = 0. Pure C: I leads V by 90° (ICE). Pure L: I lags V by 90° (ELI).
- XC = 1/(2πfC), XL = 2πfL, Z = √(R2 + (XL − XC)2).
- Resonance: XL = XC, fr = 1/(2π√(LC)).
- Average power P = Vrms Irms cosφ; cosφ is the power factor.
- EM spectrum order: Radio → Microwave → IR → Visible → UV → X-rays → Gamma.