Electronics Handbook/Circuits/Current Divider

Current Divider

If two elements are in parallel, the voltage across them must be the same, but the current divides according to the resistances. A simple circuit with two (or more) resistors in parallel with a source is called a current divider.

Figure B: Parallel Resistors.

Mathmatic Formula

If a voltage V appears across the resistors in Figure B with only $R_{1}$ and $R_{2}$ for the moment then the current flowing in the circuit, before the division, i is according to Ohms Law.

i = \frac{V}{R_{e q}}

Using the equivalent resistance for a parallel combination of resistors is

i = \frac{V (R_{1} + R_{2})}{R_{1} R_{2}}

(1)

The current through $R_{1}$ according to Ohms Law is

i_{1} = \frac{V}{R_{1}}

(2)

Dividing equation (2) by (1)

i_{1} = \frac{i R_{2}}{R_{2} + R_{1}}

Similarly

i_{2} = \frac{i R_{1}}{R_{2} + R_{1}}

In general with n Resistors the current $i_{x}$ is

i_{x} = \frac{i R_{1} R_{2} \dots R_{n}}{(R_{2} \dots R_{n} + \dots + R_{1} \dots R_{n - 1}) R_{x}}

Or possibly more simply

\frac{i_{x}}{i} = \frac{R_{e q}}{R_{x}}

Where

R_{e q} = \frac{R_{1} \dots R_{n}}{R_{2} \dots R_{n} + \dots + R_{1} \dots R_{n - 1}}

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Electronics Handbook/Circuits/Current Divider

Current Divider

Mathmatic Formula

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