Question

How do you calculate the output current in a current divider circuit?

Answer 1

To calculate the output current in a current divider circuit, you can use the current divider rule. The current divider rule allows you to determine the amount of current flowing through a particular branch in a parallel circuit. This rule is particularly useful when you have multiple resistors connected in parallel, and you want to find the current flowing through a specific resistor.

The current divider rule is expressed as follows:


out
=

in
×

other

other
+

known
I
out
    ​

=
R
other
    ​

+R
known
    ​

I
in
    ​

×R
other
    ​

    ​


Where:


out
I
out
    ​

 is the output current you want to calculate.

in
I
in
    ​

 is the total current flowing into the parallel branches (current source current).

other
R
other
    ​

 is the resistor value of the other branch (the one that you are not interested in calculating the current through).

known
R
known
    ​

 is the resistor value of the branch you want to find the current through.

Here's a step-by-step process to calculate the output current using the current divider rule:

Identify the current source and the parallel branches in the circuit.
Determine the total current flowing into the parallel branches (

in
I
in
    ​

) from the current source using other circuit analysis techniques (e.g., Kirchhoff's current law).
Identify the resistor value (

known
R
known
    ​

) for which you want to calculate the current.
Find the resistor value (

other
R
other
    ​

) of the other branch that you are not interested in calculating the current through.
Plug the values into the current divider rule formula and calculate

out
I
out
    ​

.

Remember that the current divider rule assumes an ideal situation with ideal components (i.e., no wire resistances or internal component resistances). In practice, you may need to consider the tolerance and potential variations in component values for accurate results.