The equation for each of the

**impedances in parallel**is

**u1 = Z1⋅i1; u2 = Z2⋅i2, u3 = Z3⋅i3 ... un = Zn⋅in**

In addition, equality is also fulfilled

**u1 = u2 = u3 = ... = un = u**

## Resistors in parallel and Intensity Divider

### Parallel impedance association

By applying the first Kirchhoff law to the impedance association in parallel you get

**i = i1 + i2 + i3 + ... + in = u1Z1 + u2Z2 + u3Z3 + ... + unZn**

Since the voltage applied to all the impedances is the same for all of them, it results

**i = (1Z1 + 1Z2 + 1Z3 + ... + 1Zn) ⋅u**

If the parallel association of impedances was equivalent to a single impedance (Zeq = Zparallel), applying Kirchhoff's law would result

**i = uZparallel**

Comparing both expressions, it is concluded that

**1Zparallel = 1Z1 + 1Z2 + 1Z3 + ... + 1Zn**

If all the impedances in parallel were resistors, it would be obtained that

**1Rparallel = 1R1 + 1R2 + 1R3 + ... + 1Rn**

Analogously, if all the impedances were coils without coupling, one would obtain

**1Lparallel = 1L1 + 1L2 + 1L3 + ... + 1Ln**

In the case that all the impedances were capacitors, we have

**Cparallel = C1 + C2 + C3 + ... + Cn**

In addition to obtaining the equivalent parallel impedance, it is also important to establish the relationship between the intensity of each of the impedances that make up the equivalent parallel impedance, ij, and the intensity that crosses the equivalent parallel impedance, i. The result of dividing member by member the equations of each impedance by the equivalent parallel impedance equation results

ij = 1Zj1Zparalelo⋅i

This expression shows that "the total current incoming to the set of impedances connected in parallel is divided among them inversely proportional to their value", that is why the circuit of figure 1 is known as an intensity divider.

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