Current divider
circuits
Let's analyze a simple parallel circuit,
determining the branch currents through individual
resistors:
Knowing that voltages across all components
in a parallel circuit are the same, we can fill in our
voltage/current/resistance table with 6 volts across the top
row:
Using Ohm's Law (I=E/R) we can calculate
each branch current:
Knowing that branch currents add up in
parallel circuits to equal the total current, we can arrive
at total current by summing 6 mA, 2 mA, and 3 mA:
The final step, of course, is to figure
total resistance. This can be done with Ohm's Law (R=E/I) in
the "total" column, or with the parallel resistance formula
from individual resistances. Either way, we'll get the same
answer:
Once again, it should be apparent that the
current through each resistor is related to its resistance,
given that the voltage across all resistors is the same.
Rather than being directly proportional, the relationship
here is one of inverse proportion. For example, the current
through R_{1} is half as much as the current through
R_{3}, which has twice the resistance of R_{1}.
If we were to change the supply voltage of
this circuit, we find that (surprise!) these proportional
ratios do not change:
The current through R_{1} is still
exactly twice that of R_{2}, despite the fact that
the source voltage has changed. The proportionality between
different branch currents is strictly a function of
resistance.
Also reminiscent of voltage dividers is the
fact that branch currents are fixed proportions of the total
current. Despite the fourfold increase in supply voltage,
the ratio between any branch current and the total current
remains unchanged:
For this reason a parallel circuit is often
called a current divider for its ability to
proportion  or divide  the total current into fractional
parts. With a little bit of algebra, we can derive a formula
for determining parallel resistor current given nothing more
than total current, individual resistance, and total
resistance:
The ratio of total resistance to individual
resistance is the same ratio as individual (branch) current
to total current. This is known as the current divider
formula, and it is a shortcut method for determining
branch currents in a parallel circuit when the total current
is known.
Using the original parallel circuit as an
example, we can recalculate the branch currents using this
formula, if we start by knowing the total current and total
resistance:
If you take the time to compare the two
divider formulae, you'll see that they are remarkably
similar. Notice, however, that the ratio in the voltage
divider formula is R_{n} (individual resistance)
divided by R_{Total}, and how the ratio in the
current divider formula is R_{Total} divided by R_{n}:
It is quite easy to confuse these two
equations, getting the resistance ratios backwards. One way
to help remember the proper form is to keep in mind that
both ratios in the voltage and current divider equations
must equal less than one. After all these are divider
equations, not multiplier equations! If the fraction
is upsidedown, it will provide a ratio greater than one,
which is incorrect. Knowing that total resistance in a
series (voltage divider) circuit is always greater than any
of the individual resistances, we know that the fraction for
that formula must be R_{n} over R_{Total}.
Conversely, knowing that total resistance in a parallel
(current divider) circuit is always less then any of the
individual resistances, we know that the fraction for that
formula must be R_{Total} over R_{n}.
Current divider circuits also find
application in electric meter circuits, where a fraction of
a measured current is desired to be routed through a
sensitive detection device. Using the current divider
formula, the proper shunt resistor can be sized to
proportion just the right amount of current for the device
in any given instance:

REVIEW:

Parallel circuits proportion, or "divide,"
the total circuit current among individual branch
currents, the proportions being strictly dependent upon
resistances: I_{n} = I_{Total} (R_{Total}
/ R_{n})
