Voltage divider circuits
Let's analyze a simple series circuit, determining the voltage
drops across individual resistors:
From the given values of individual resistances, we can determine
a total circuit resistance, knowing that resistances add in series:
From here, we can use Ohm's Law (I=E/R) to determine the total
current, which we know will be the same as each resistor current,
currents being equal in all parts of a series circuit:
Now, knowing that the circuit current is 2 mA, we can use Ohm's
Law (E=IR) to calculate voltage across each resistor:
It should be apparent that the voltage drop across each resistor
is proportional to its resistance, given that the current is the
same through all resistors. Notice how the voltage across R2
is double that of the voltage across R1, just as the
resistance of R2 is double that of R1.
If we were to change the total voltage, we would find this
proportionality of voltage drops remains constant:
The voltage across R2 is still exactly twice that of R1's
drop, despite the fact that the source voltage has changed. The
proportionality of voltage drops (ratio of one to another) is
strictly a function of resistance values.
With a little more observation, it becomes apparent that the
voltage drop across each resistor is also a fixed proportion of the
supply voltage. The voltage across R1, for example, was
10 volts when the battery supply was 45 volts. When the battery
voltage was increased to 180 volts (4 times as much), the voltage
drop across R1 also increased by a factor of 4 (from 10
to 40 volts). The ratio between R1's voltage drop
and total voltage, however, did not change:
Likewise, none of the other voltage drop ratios changed with the
increased supply voltage either:
For this reason a series circuit is often called a voltage
divider for its ability to proportion -- or divide -- the total
voltage into fractional portions of constant ratio. With a little
bit of algebra, we can derive a formula for determining series
resistor voltage drop given nothing more than total voltage,
individual resistance, and total resistance:
The ratio of individual resistance to total resistance is the
same as the ratio of individual voltage drop to total supply voltage
in a voltage divider circuit. This is known as the voltage
divider formula, and it is a short-cut method for determining
voltage drop in a series circuit without going through the current
calculation(s) of Ohm's Law.
Using this formula, we can re-analyze the example circuit's
voltage drops in fewer steps:
Voltage dividers find wide application in electric meter
circuits, where specific combinations of series resistors are used
to "divide" a voltage into precise proportions as part of a voltage
measurement device.
One device frequently used as a voltage-dividing component is the
potentiometer, which is a resistor with a movable element
positioned by a manual knob or lever. The movable element, typically
called a wiper, makes contact with a resistive strip of
material (commonly called the slidewire if made of resistive
metal wire) at any point selected by the manual control:
The wiper contact is the left-facing arrow symbol drawn in the
middle of the vertical resistor element. As it is moved up, it
contacts the resistive strip closer to terminal 1 and further away
from terminal 2, lowering resistance to terminal 1 and raising
resistance to terminal 2. As it is moved down, the opposite effect
results. The resistance as measured between terminals 1 and 2 is
constant for any wiper position.
Shown here are internal illustrations of two potentiometer types,
rotary and linear:
Some linear potentiometers are actuated by straight-line motion
of a lever or slide button. Others, like the one depicted in the
previous illustration, are actuated by a turn-screw for fine
adjustment ability. The latter units are sometimes referred to as
trimpots, because they work well for applications requiring a
variable resistance to be "trimmed" to some precise value. It should
be noted that not all linear potentiometers have the same terminal
assignments as shown in this illustration. With some, the wiper
terminal is in the middle, between the two end terminals.
The following photograph shows a real, rotary potentiometer with
exposed wiper and slidewire for easy viewing. The shaft which moves
the wiper has been turned almost fully clockwise so that the wiper
is nearly touching the left terminal end of the slidewire:
Here is the same potentiometer with the wiper shaft moved almost
to the full-counterclockwise position, so that the wiper is near the
other extreme end of travel:
If a constant voltage is applied between the outer terminals
(across the length of the slidewire), the wiper position will tap
off a fraction of the applied voltage, measurable between the wiper
contact and either of the other two terminals. The fractional value
depends entirely on the physical position of the wiper:
Just like the fixed voltage divider, the potentiometer's voltage
division ratio is strictly a function of resistance and not
of the magnitude of applied voltage. In other words, if the
potentiometer knob or lever is moved to the 50 percent (exact
center) position, the voltage dropped between wiper and either
outside terminal would be exactly 1/2 of the applied voltage, no
matter what that voltage happens to be, or what the end-to-end
resistance of the potentiometer is. In other words, a potentiometer
functions as a variable voltage divider where the voltage division
ratio is set by wiper position.
This application of the potentiometer is a very useful means of
obtaining a variable voltage from a fixed-voltage source such as a
battery. If a circuit you're building requires a certain amount of
voltage that is less than the value of an available battery's
voltage, you may connect the outer terminals of a potentiometer
across that battery and "dial up" whatever voltage you need between
the potentiometer wiper and one of the outer terminals for use in
your circuit:
When used in this manner, the name potentiometer makes
perfect sense: they meter (control) the potential
(voltage) applied across them by creating a variable voltage-divider
ratio. This use of the three-terminal potentiometer as a variable
voltage divider is very popular in circuit design.
Shown here are several small potentiometers of the kind commonly
used in consumer electronic equipment and by hobbyists and students
in constructing circuits:
The smaller units on the very left and very right are designed to
plug into a solderless breadboard or be soldered into a printed
circuit board. The middle units are designed to be mounted on a flat
panel with wires soldered to each of the three terminals.
Here are three more potentiometers, more specialized than the set
just shown:
The large "Helipot" unit is a laboratory potentiometer designed
for quick and easy connection to a circuit. The unit in the
lower-left corner of the photograph is the same type of
potentiometer, just without a case or 10-turn counting dial. Both of
these potentiometers are precision units, using multi-turn
helical-track resistance strips and wiper mechanisms for making
small adjustments. The unit on the lower-right is a panel-mount
potentiometer, designed for rough service in industrial
applications.
- REVIEW:
- Series circuits proportion, or divide, the total supply
voltage among individual voltage drops, the proportions being
strictly dependent upon resistances: ERn = ETotal
(Rn / RTotal)
- A potentiometer is a variable-resistance component with three
connection points, frequently used as an adjustable voltage
divider.
|
