Parallel Resistances and Current Divider

Parallel circuits are circuits that have more than one path for current flow.

One of the rules for parallel circuits states that the total current flow in the circuit is equal to the sum of the currents through all of the branches.

Consider the circuit shown in Figure 10.2, the source current is

Figure 10.2 Parallel Circuit for a Current Divider

 (10.2)


Where RT is the equivalent resistance of R1, R2, and R3 connected in parallel and is is the total current entering the combination.

It is clear from the Figure 10.2 that the current is is divided between the three resistors.

 (10.3)

Rules for Parallel Circuits:

  • The voltage is the same across any branch of a parallel circuit.

  • The source (total) current is the sum of the individual currents through each path in the circuit.

  • The reciprocal of the total resistance is the sum of the reciprocals of the branch resistances.
               

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