Capacitor Current and Time-Varying Capacitance
For a lumped capacitor q=Cv, differentiating gives i=C dv/dt+v dC/dt; the familiar i=C dv/dt assumes constant capacitance and a consistent passive sign convention.
Why this shows up in the exam
required voltage ramp for a current · moving dielectric or liquid level · time-dependent plate geometry
Learn the idea
Capacitor current is the time derivative of charge, including changes in voltage or capacitance. A capacitor can carry current while its stored charge changes even though no conduction crosses the dielectric. If geometry changes, C itself can vary with time.
🧠 Memory hook: Differentiate CV; do not assume C is constant.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- i = d(Cv)/dt = C dv/dt + v dC/dt — differentiable C(t), v(t)
- i = C dv/dt — constant capacitance
How to approach it
- 1Write q=Cv
- 2Decide whether C varies
- 3Differentiate before substituting numbers
Common slip-ups that cost marks
- •Using i=V/C
- •Dropping v dC/dt for moving geometry
- •Ignoring sign convention
🌟 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.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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