Problems solving in electrical engineering (Theoretical Foundations of Electrical Engineering), circuit analysis (Foundations of Circuit Analysis) and electronics
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Theoretical foundations of electrical engineering

Problems solving in electrical engineering – Current divider

General scheme of the Current divider is shown in Fig.1.

Problems solving in electrical engineering – Current divider

Fig.1 –General scheme of the current divider

The scheme shows that the current I is divided on resistances into currents I1, I2, I3, …, In (n is the number of resistors).

We know the current I and resistors resistances. It is necessary to find currents I1, I2, I3, …, In.

We make general formula, allowing to find any of these currents.

To find the current I we replace all resistors with equivalent resistors (Fig. 2).

Problems solving in electrical engineering – Current divider

Fig.2 – Equivalent circuit of resistors

We find the resistance of the equivalent resistor from the formula of parallel connection of resistances:

Problems solving in electrical engineering – Current divider(1)

Voltage U is applied to the resistance of the equivalent resistor, hence, through this resistor the current I will flow, which can be found by Ohm’s law:

Problems solving in electrical engineering – Current divider(2)

We know the values of the current I and the resistance of the equivalent resistor, so we express U from the formula (2) and substitute the equivalent resistor from the formula (1):

Problems solving in electrical engineering – Current divider(3)

Make general formula with the help of which any current in any branch can be found.

We find the value of the current in the branch by Ohm’s law

Problems solving in electrical engineering – Current divider(4)

We know the resistance of the resistor Ri (resistor in the branch), substitute in the formula U from the formula (3):

Problems solving in electrical engineering – Current divider5)

That is, according to the formula

Problems solving in electrical engineering – Current divider(6)

you can find current in any branch.

In the case with 2 resistances (n=2) the formula is greatly simplified.

Scheme of the current divider with two resistors is shown in Fig. 3.

Problems solving in electrical engineering – Current divider

Fig.3 –Scheme of the current divider with two resistors

Formula (6) becomes:

Problems solving in electrical engineering – Current divider(6)

By this formula we find currents I1, I2:

Problems solving in electrical engineering – Current divider(7)

Final formula:

Problems solving in electrical engineering – Current divider(8)

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