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DC Circuits

# Current Dividers

A current divider may be considered basically as some combination of impedances that will cause the output current of a network to be less than the input current. We shall restrict our discussion of current dividers to their simplest forms.

Consider figure below, which shows a line current *I*_{t}, feeding two branches
so that *I*_{t} splits into *I*_{R1} and *I*_{R2}.
We should like to find a simple relationship between *I*_{R2} and *I*_{t}
in terms of the branch resistances *R*_{1} and *R*_{2}.

Since *R*_{1} and *R*_{2} are in parallel, the voltage across them must be the same. Therefore, *I*_{R1}*R*_{1} = *I*_{R2}*R*_{2}.
We want *I*_{t} and not *I*_{R1} in our final expression. Therefore,
let us express *I*_{R1} in terms of *I*_{t}. Obviously,
*I*_{t} = *I*_{R1} + *I*_{R2}. Therefore,
*I*_{R1} = *I*_{t} - *I*_{R2}. By substitution,
(*I*_{t} - *I*_{R2})*R*_{1} = *I*_{R2}*R*_{2}. Solving for *I*_{R2}, we obtain

At this point, we want to show what a simple phrase such as "solving for *I*_{R2}" implies.
The following algebraic manipulations were involved

Therefore

which as stated above yields

To continue with our problem, it can be shown similarly that

Notice here that, in this type of formula, as compared with that for the voltage divider, the numerator contains the shunt impedance, whose current we are *not* interested in.