Displacement Current in a Capacitor
For a linear capacitor with constant capacitance C, charge is q = CV and the charging current equals C dV/dt. In an ideal capacitor this is also the displacement current through the complete inter-plate surface.
Why this shows up in the exam
Finding voltage slew rate from capacitor current · Calculating AC current through a capacitor · Relating capacitor geometry to field-current response
Learn the idea
For a capacitor, displacement current follows the rate of voltage change and the capacitance. A capacitor draws more current when its voltage changes faster. Larger plate area or permittivity raises capacitance, while larger separation lowers it, so geometry controls the displacement current for a given voltage change.
🧠 Memory hook: Capacitor current tracks how fast voltage changes.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I_d = C dV/dt — instantaneous displacement current for constant capacitance
- C = epsilon A/d — parallel-plate capacitance neglecting edge effects
- I₀ = omega C V₀ — current amplitude for V = V₀ sin(omega t)
How to approach it
- 1Decide whether values are instantaneous, peak, or rms
- 2Use I = C dV/dt or I₀ = omega C V₀
- 3Substitute C = epsilon A/d only when geometry is needed
Common slip-ups that cost marks
- •Using V instead of dV/dt
- •Mixing peak and rms voltage or current
- •Forgetting to convert microfarads and angular frequency to SI units
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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