In a current divider circuit, the goal is to calculate the amount of current flowing through each branch of a parallel circuit configuration. The formula to calculate the output current in a current divider circuit is:
out
=
in
×
total
branch
I
out
=I
in
×
R
branch
R
total
Where:
out
I
out
is the output current you want to calculate.
in
I
in
is the total current entering the parallel branches (input current).
total
R
total
is the total resistance of all parallel branches combined.
branch
R
branch
is the resistance of the specific branch for which you want to calculate the output current.
Here's a step-by-step explanation of how to use this formula:
Calculate the total resistance (
total
R
total
) of all the parallel branches combined. If you have two resistors in parallel, their total resistance is given by the formula:
1
total
=
1
1
+
1
2
R
total
1
=
R
1
1
+
R
2
1
For more than two resistors, you would continue adding the reciprocals of their resistances.
Once you have the total resistance (
total
R
total
), choose the specific branch for which you want to calculate the output current.
Plug the values of
in
I
in
,
total
R
total
, and
branch
R
branch
into the formula:
out
=
in
×
total
branch
I
out
=I
in
×
R
branch
R
total
This will give you the output current (
out
I
out
) through the chosen branch.
Remember that the sum of the currents through all parallel branches will always equal the total input current (
in
I
in
) due to the conservation of charge.
Also, keep in mind that this formula assumes ideal conditions and doesn't account for factors like wire resistance or component tolerances, which can affect the actual currents in a real circuit.