To succeed in electronics you must have a good understanding of, even a good feeling for, the concept of voltage or potential difference. Remember, the dimensions of voltage are joules/coulomb; voltage at a point is a measure of the potential energy per unit charge of a charge at that point relative to any point where the voltage is zero. There is a one-to-one correspondence with the potential energy of mass in a gravitational field.

PE = MgH

M corresponds to charge, Q, and gH corresponds to voltage, V. The height, H, is measured from some point which arbitrarily is assigned H = 0, for example sea level. Similarly, we will usually arbitrarily assign some point in our circuit the value V = 0. Thus when we speak of the voltage at a point in our circuit, we really mean the difference in potential energy per unit charge between that point and the reference point. We refer to this reference point as ground, and the zero of potential as ground potential. The potential difference between two points, a and b, is written V_ab = V_a - V_b, where V_a is the potential at point a relative to ground and V_b is the potential at point b relative to ground.

There are three passive linear elements of importance in electronics. Each of them develops a potential difference or voltage (V) across its two terminals which is proportional to some function of the charge associated with the element.

The voltage is given in volts, the charge in coulombs and the capacitance in farads, although typical values are in microfarads (m f) or picofarads (pf), micro indicating 10^-6, pico indicating 10^-12. One coulomb of charge on a capacitor of one farad would create a potential difference of one volt.

(2)

The current is given in amperes or amps, the resistance in ohms. A current of one ampere is equal to one coulomb per second. When one ampere flows through one ohm, there is a voltage drop of one volt across the resistor.

(3)

The inductance is given in henries.

It should be noted that there are no pure resistors, pure capacitors, or pure inductors. Any element always has resistance, capacitance and inductance. One aspect will greatly dominate the other two in most cases of interest.

We will concentrate first on resistors and currents. Relationship (2):

is known as Ohm's law and holds with great precision for many types of materials. The important thing for the designer to know is that resistors are probably the cheapest, most dependable and most precise devices available to the electronics circuit designer. Resistors should be made the critical elements in circuits whenever possible.

A resistor is indicated schematically by the following:

Note that the current always flows from higher to lower potential. V_a is greater than V_b. This is often indicated by the use of + and - signs even though both V_a and V_b may be plus (or minus) relative to ground. Now suppose you have two resistors in series.

Let us digress to note that if a current I flows through R₁, to great accuracy, the same current must flow through R₂ also, assuming that there is no additional path through which it can flow. The reason is that electromagnetic forces are large. Suppose for a moment that the current I flowing through R₁ is one milliamp (10^-3 amp). Suppose that for one second, current accumulated at b without flowing through R₂. Then there would be 10^-3 amps x 1 sec = 10^-3 coulombs at b. If a similar but opposite charge were to accumulate one cm away, the force between them would be:

which is about 10,000 tons! Thus we usually are able to assume that if a charge Q flows into an element, it also flows out of it.

Now the current I is given by:

(4)

What we want to know is, what single resistance is equivalent to R₁ and R₂, i.e.:

Substituting from (4):

Thus two series resistors R₁ and R₂ are equivalent to a single resistor of value R₁ + R_2.

What single resistor R_eq placed between potentials V_a and V_b would have a current I = I₁ + I₂ flow through it? Show that in this case:

0 = -5V + 10 W I₁ + 30 W (I₁ - I₂) + 20 W I₁

It often happens that we have a power supply, a battery or even a time-varying signal generator that gives us one voltage, but we want another smaller voltage. We often obtain the new potential or voltage with a pair of resistors. In our analysis we will refer all voltages to a fixed potential which we call ground or zero potential. The

Now:

(Ans. R_X = 100 W )

(Ans. R_X = 200 W )

Note the important point that if a load which draws current (in this case the 200 W ) is connected to a voltage divider, the simple result of the previous page does not hold UNLESS the load and R_x IN PARALLEL are considered to be R₂.

THOUSANDS OF EXAM ERRORS HAVE RESULTED FROM STUDENTS FORGETTING THAT THE SIMPLE VOLTAGE DIVIDER EQUATION ONLY HOLDS FOR AN UNLOADED VOLTAGE DIVIDER!