Current divider
PARTS AND MATERIALS
CROSS-REFERENCES
Lessons In Electric Circuits, Volume
1, chapter 6: "Divider Circuits and Kirchhoff's Laws"
LEARNING OBJECTIVES
SCHEMATIC DIAGRAM
ILLUSTRATION
Normally, it is considered improper to
secure more than two wires under a single terminal strip
screw. In this illustration, I show three wires joining at
the top screw of the rightmost lug used on this strip. This
is done for the ease of proving a concept (of current
summing at a circuit node), and does not represent
professional assembly technique.
The non-professional nature of the
"free-form" construction method merits no further comment.
INSTRUCTIONS
Once again, I show different methods of
constructing the same circuit: breadboard, terminal strip,
and "free-form." Experiment with all these construction
formats and become familiar with their respective advantages
and disadvantages.
Select three resistors from your resistor
assortment and measure the resistance of each one with an
ohmmeter. Note these resistance values with pen and paper,
for reference in your circuit calculations.
Connect the three resistors in parallel to
and each other, and with the 6-volt battery, as shown in the
illustrations. Measure battery voltage with a voltmeter
after the resistors have been connected to it, noting this
voltage figure on paper as well. It is advisable to measure
battery voltage while it's powering the resistor circuit
because this voltage may differ slightly from a no-load
condition.
Measure voltage across each of the three
resistors. What do you notice? In a series circuit,
current is equal through all components at any given
time. In a parallel circuit, voltage is the common
variable between all components.
Use Ohm's Law (I=E/R) to calculate current
through each resistor, then verify this calculated value by
measuring current with a digital ammeter. Place the red
probe of the ammeter at the point where the positive (+)
ends of the resistors connect to each other and lift one
resistor wire at a time, connecting the meter's black probe
to the lifted wire. In this manner, measure each resistor
current, noting both the magnitude of the current and the
polarity. In these illustrations, I show an ammeter used to
measure the current through R1:
Measure current for each of the three
resistors, comparing with the current figures calculated
previously. With the digital ammeter connected as shown, all
three indications should be positive, not negative.
Now, measure total circuit current, keeping
the ammeter's red probe on the same point of the circuit,
but disconnecting the wire leading to the positive (+) side
of the battery and touching the black probe to it:
Note both the magnitude and the sign of the
current as indicated by the ammeter. Add this figure
(algebraically) to the three resistor currents. What do you
notice about the result that is similar to the Kirchhoff's
Voltage Law experiment? Kirchhoff's Current Law is to
currents "summing" at a point (node) in a circuit, just as
Kirchhoff's Voltage Law is to voltages adding in a series
loop: in both cases, the algebraic sum is equal to zero.
This Law is also very useful in the
mathematical analysis of circuits. Along with Kirchhoff's
Voltage Law, it allows us to generate equations describing
several variables in a circuit, which may then be solved
using a variety of mathematical techniques.
Now consider the four current measurements
as all positive numbers: the first three representing the
current through each resistor, and the fourth representing
total circuit current as a positive sum of the three
"branch" currents. Each resistor (branch) current is a
fraction, or percentage, of the total current. This is why a
parallel resistor circuit is often called a current
divider.
Disconnect the battery from the rest of the
circuit, and measure resistance across the parallel
resistors. You may read total resistance across any
of the individual resistors' terminals and obtain the same
indication: it will be a value less than any of the
individual resistor values. This is often surprising to new
students of electricity, that you read the exact same
(total) resistance figure when connecting an ohmmeter across
any one of a set of parallel-connected resistors. It
makes sense, though, if you consider the points in a
parallel circuit in terms of electrical commonality. All
parallel components are connected between two sets of
electrically common points. Since the meter cannot
distinguish between points common to each other by way of
direct connection, to read resistance across one resistor is
to read the resistance of them all. The same is true for
voltage, which is why battery voltage could be read across
any one of the resistors as easily as it could be read
across the battery terminals directly.
If you divide the battery voltage
(previously measured) by this total resistance figure, you
should obtain a figure for total current (I=E/R) closely
matching the measured figure.
The ratio of resistor current to total
current is the same as the ratio of total resistance to
individual resistance. For example, if a 10 kΩ resistor is
part of a current divider circuit with a total resistance of
1 kΩ, that resistor will conduct 1/10 of the total current,
whatever value that current total happens to be.
COMPUTER SIMULATION
Schematic with SPICE node numbers:
Ammeters in SPICE simulations are actually
zero-voltage sources inserted in the paths of electron flow.
You will notice the voltage sources Vir1, Vir2,
and Vir3 are set to 0 volts in the netlist. When
electrons enter the negative side of one of these "dummy"
batteries and out the positive, the battery's current
indication will be a positive number. In other words, these
0-volt sources are to be regarded as ammeters with the red
probe on the long-line side of the battery symbol and the
black probe on the short-line side.
Netlist (make a text file containing the
following text, verbatim):
Current divider
v1 1 0
r1 3 0 2k
r2 4 0 3k
r3 5 0 5k
vitotal 2 1 dc 0
vir1 2 3 dc 0
vir2 2 4 dc 0
vir3 2 5 dc 0
.dc v1 6 6 1
.print dc i(vitotal) i(vir1) i(vir2) i(vir3)
.end
When run, SPICE will print a line of text
containing four current figures, the first current
representing the total as a negative quantity, and the other
three representing currents for resistors R1, R2,
and R3. When algebraically added, the one
negative figure and the three positive figures will form a
sum of zero, as described by Kirchhoff's Current Law. |