Current Sources in Parallel

Electrical Circuit Analysis > Methods of Analysis > Current Sources

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We found that voltage sources of different terminal voltages cannot be placed in parallel because of a violation of Kirchhoff's voltage law. Similarly,

Current sources of different values cannot be placed in series due to a violation of Kirchhoff's current law.

However, current sources can be placed in parallel just as voltage sources can be placed in series. In general,

Two or more current sources in parallel can be replaced by a single current source having a magnitude determined by the difference of the sum of the currents in one direction and the sum in the opposite direction. The new parallel internal resistance is the total resistance of the resulting parallel resistive elements.

Consider the following example.

Example 1: Reduce the parallel current sources in [Fig. 1] to a single current source.

Fig 1: Parallel current sources for Example 1.

Solution: The net source current is

$$I = 10 A - 6 A = 4 A$$

with the direction being that of the larger source. The net internal resistance is the parallel combination of resistances, $R_1$ and $R_2$:

$$R_p = 3 Ω || 6 Ω = 2 Ω$$

The reduced equivalent appears in [Fig. 2].

Fig. 2: Reduced equivalent for the configuration of Fig. 1.

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