# Current Divider

fact

Just like the voltage divider uses two series resistors to split the voltage into two parts the current divider uses two parallel resistors in order to split incoming current into two parts

fact

The current \(I_1\) through resistor \(R_1\) is given by: \(I_1 = I_t \frac{R_2}{R_1 + R_2}\).

example

Find the current \(I_1\) in the circuit below

We just apply our formula and find: \(I_1 = I_t \frac{R_2}{R_1 + R_2} = 5 \frac{1000}{200 + 1000} = 4.17A\)fact

The higher the resistance \(R_1\) relative to the resistor \(R_2\) the lower the current through \(R_1\).

fact

If \(R_1 = R_2\) then \(I_1 = I_2 = \frac{I_t}{2}\)

fact

If there are more than two resistors then all of the resistors that aren't on the path whose current we want need to be combined into a single equivalent resistor (see example below).

example

Find the current \(I_1\) in the circuit below

We need to combine resistors \(R_2\) and \(R_3\) into an equivalent resistor \(R_{eq}\) so that we get the form with only two resistors. \(R_{eq} = \frac{R_2\times R_3}{R_2 + R_3} = \frac{100\times 200}{100 + 200} = 66.67\Omega\) Now we just use our above formula: \(I_1 = I_t \frac{R_{eq}}{R_1 + R_{eq}} = 2 \frac{66.67\Omega}{500 + 66.67\Omega} = 235mA\)
practice problems