Capacitors and Inductors Have Ohms

Capacitors are basically two foil plates separated by insulation. Inductors are basically coiled-up wire. That should make capacitors infinity ohms and inductors just the wire’s resistance, like below 2 ohms. This is true at DC. But it isn't true at AC. We will return to this below.*

(As we get into equations, let’s review that C is capacitance, measured in farads, and current is I, the I being "intensity" and measured in amps.)

We know that resistors have ohms, like 100 ohms or 10,000 ohms. Resistors get hot when current goes through them, like...

Resistance is why an iron, stove, or coffee percolator gets hot. A stove passing 5A at 220V has power of P = 220 * 5 = 1100 watts.

*There is no argument that capacitors are measured in microfarads or picofarads and inductors are measured in microhenrys. But they both pass current at frequencies as if they have ohms.

Two strange things about capacitance and inductance are that 1) they don’t get hot by passing current and 2) their interesting properties are from their ohms, not their microfarads or microhenries.

Since capacitors are used more than inductors, let’s talk about capacitors. Audio- and radio-frequency amplifiers are usually "cap-coupled" between transistors, like * in the schematic below.

You calculate the capacitance value based on the lowest frequency of the amplifier, like 20Hz for an audio amplifier, and also based on the input resistance of the next transistor.

It is true that a capacitor or inductor has ohms, but you will eventually need to know that there is a phase shift between voltage and current for these parts. For sine waves, a capacitor’s current leads the voltage by 90 degrees, and an inductor’s current lags the voltage by 90 degrees. Compare this to a resistor: the voltage and current sines are in phase.

C=It/V

There is an additional equation for capacitors used in timing circuits and power supplies. The equation is C=It/V. For a power supply, the t for 60 Hertz is 1/f=.0167s.

Let’s say you want the capacitor to droop no more than .3V when current is 2A.

C = 2 .0167 / .3 = 111,000μF

Choose this or higher for your filter capacitor. It is $32 for 110,000uF, 16V in the Mouser catalog, 3" diam x 4.5" long. This is not good! What can we do to get a more reasonable cap?

The instructor gives some guidance. We need to use a bridge rectifier, and the frequency goes to 120Hz, for t=.0083s. We need to put in a transistor series regulator following the filter capacitor so the ripple voltage on the filter cap doesn’t matter (as long as the transistor does not saturate). We might be able to let the cap ripple 5V. Let’s try the calculation again.

C = It/V = 2 .0083 / 5 = 3300μF

This is much better, $1.40.