Finding impedance of rlc parallel ckt

[umed9]

in most of the books i have seen that while finding an impedance for an parallel RLC circuit first they find the individual admittance of each of the element the after summation of these they take reciprocal to find the impedance
why is it done like that can't we find the impedance in a normal way of finding resistance in parallel circuit

 

[umed9]

the result does comes different by two methods

 

[berkeman]

in most of the books i have seen that while finding an impedance for an parallel RLC circuit first they find the individual admittance of each of the element the after summation of these they take reciprocal to find the impedance
why is it done like that can't we find the impedance in a normal way of finding resistance in parallel circuit

the result does comes different by two methods

Can you show us how you get two different results using the two different methods? I would not expect that...

 

[meBigGuy]

If you add the admittance and convert to impedance you will get the same result as working out the impedance of 3 parallel elements. Just do the math both ways with Z1, Z2, and Z3 and if they don't agree, do it again until you find the math error. 1/((1/Z1) + (1/Z2) + (1/Z3)) = Zt and the long form for Z1||Z2||Z3 = Zt where Z1||Z2 is (Z1*Z2)/(Z1+Z2)

 

[alphy]

The reason for finding the impedance of an RLC parallel circuit by first finding the individual admittances of each element and then taking their reciprocal is because it is a more accurate and efficient method. In a parallel circuit, the impedance is given by the reciprocal of the sum of the individual admittances. This is because in a parallel circuit, the current is divided among the different branches, and the total impedance is affected by the admittances of all the branches.

By calculating the individual admittances and then taking their reciprocal, we are taking into account the effects of the different elements on the total impedance. This method also allows us to easily incorporate the effects of capacitors and inductors, which have complex admittances, into the calculation.

On the other hand, finding the total impedance in a parallel circuit by using the traditional method of finding resistance in a parallel circuit may not give an accurate result. This is because the traditional method only takes into account the resistance of the elements and does not consider the effects of capacitors and inductors.

In conclusion, while it may seem more complicated to first find the individual admittances and then take their reciprocal, it is a more accurate and efficient method for finding the impedance of an RLC parallel circuit.