Parallel ac Networks

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For the representative parallel ac network of [Fig. 1],

Fig. 1: Parallel ac network.

the total impedance or admittance is determined as described in the previous section, and the source current is determined by Ohm's law as follows:

$$I = {E \over Z_T} = E Y_T$$

Since the voltage is the same across parallel elements, the current through each branch can then be found through another application of Ohm's law:

$$I_1 = {E \over Z_1} = E Y_1$$

$$I_2 = {E \over Z_2} = E Y_2$$

Kirchhoff's current law can then be applied in the same manner as employed for dc networks.

However, keep in mind that we are now dealing with the algebraic manipulation of quantities that have both magnitude and direction.

$$I - I_1 - I_2 = 0$$

$$I = I_1 + I_2 $$

The power to the network can be determined by

$$P = EI \cos \theta_T$$

where $\theta_T$ is the phase angle between E and I.
Let us now look at a few examples carried out in great detail for the first exposure.

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