## Saturday, April 18, 2015

### Resistors, Capacitors and Inductors! Oh my!

Resistors:

As you may know from the previous blogs, resistors are two terminal passive components that effectively limit current flow.  We can demonstrate resistance by recalling our previous river analogy.

The analogy suggests that water in a river is represented as 'charge'.  Water flowing in any spatial direction can be represented as current.  If you were to add rocks (resistance) in the path of the river you would effectively reduce the current flow.  This is displayed in Figure 1.

Figure 1.  River analogy for resistance

The current through a resistor equates to the potential across the resistive element divided by the resistance of the element, otherwise known as I=V/R.

The properties of a resistor connected in series or in parallel are illustrated in Figure 2.

Resistors in series

Two resistors in parallel

Resistors in parallel

Figure 2. Properties of Resistors

Power across is resistor is calculated as:

Capacitors:

Capacitors are two terminal passive components that are used to store energy in its electric field.

Recalling our river analogy, capacitors can be represented as a bucket.  If you were to bring a bucket to the river you can collect some water (charge).  The bigger the bucket (capacitance value) the more water (charge) you will be able to collect.

Figure 3.  River analogy for capacitance

In the simplest illustration, a capacitor can be represented as two parallel metal plates, as shown in Figure 4.

Figure 4. Capacitance from parallel plates

The amount of charge is dependent on the voltage across the capacitor and the capacitance value.

Q = C * V
Q [Charge in Coulombs]= C[Capacitance value]*V[Voltage across cap]

The properties of a capacitor connected in series or in parallel are illustrated in Figure 5.

Capacitors in series

Capacitors in parallel

Figure 5. Properties of Capacitors

Instantaneous current through a capacitor:

Inductors:

Inductors, also called "coils", are two terminal passive components that are used to resist changes in electrical current and stores energy in it magnetic field.

Using the river analogy again, we can illustrate the inductor as a water wheel that initially resists any big waves converting it into steady current defined by the resistance of the river path, as shown in Figure 6.

Figure 6.  River analogy for inductance

The properties of an inductor are listed in Figure 7.

Inductors in series

Two inductors in parallel

Inductors in parallel

Figure 7. Properties of Inductors

Instantaneous voltage across an inductor: