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 R1 is half as much as the current through
R3, which has twice the resistance of R1.
If we were to change the supply voltage of this circuit, we find
that (surprise!) these proportional ratios do not change:
The current through R1 is still exactly twice that of
R2, 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 short-cut
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
re-calculate 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 Rn (individual
resistance) divided by RTotal, and how the ratio in the
current divider formula is RTotal divided by Rn:
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 upside-down, 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 Rn over RTotal. 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 RTotal over Rn.
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: In = ITotal
(RTotal / Rn)
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