Capacitors
Introduction
Capacitors are arguably the most useful components an electrical engineer has at their disposal and are used everywhere from high voltage power transmission to practically every piece of electronics. They can smooth DC power supply, act as a little reservoir of charge that is a handy friend for IC’s (google decoupling capacitor for more info) and make op amps work!
At the moment, we just want to know what equations we can use and where they crop up in circuits (which is everywhere)
All About Caps
Capacitor Equations
In Physics 1B you’ll learn the nitty gritty of how a capacitor works, so don’t stress! You’ll also learn where the two important equations:
C=q/v
C = 𝜀*A/d
come from!
Series and Parallel Combinations
Think of capacitors as a very ‘voltage-y’ component. We have C times dv/dt, and parallel (i.e. same voltage) capacitors can actually have their capacitance (or C value) summed!
i.e. parallel Ceq = C1 + C2 + …
Series capacitances can be combined like parallel resistors (resistors are a ‘current-y’ component).
Energy in a Capacitor
Caps are passive, just like resistors. This means that a current entering the positive terminal (vi > 0) will charge the capacitor, and a current entering the negative terminal will mean the capacitor is supplying energy or discharging (like a mini battery).
Power = vi which can be integrated to give us the energy stored: 1/2Cv^2 (provided the initial energy is zero - imagine it has been hooked up to ground for a long time) (see derivation here)
Capacitors at AC and DC
O/C (open circuit) for DC voltage - no change in voltage therefore dv/dt = 0 and thus i = 0.
When we begin working with AC voltages, the capacitor is a S/C (short circuit) for high frequency.
Further Resources
For a very detailed explanation of caps (overkill for this ELEC1111), check out this sparkfun article.