After reading this topic you will be able to solve all kinds of complex a/c circuits in a blink . Please gimme some credit
First of all we have only learnt to solve series a/c circuits in school, so we would not be able to solve parrelel or other complex circuits unless we had taken any coaching . I had found this methos online and it is very useful for:
a)taking out resultant impedance and reactance
b)the phase angle
Heres how to do it
First of all we can assume the capacitative reactance and inductive reactance and resistance to be phasors that is rotating vectors.Now we cant add or subtract them directly as they are vectors and not scalars . We could use vector addition but we dont know the phase angle as well. If somehow we could convert them into scalars we could add and subtract them easily.
We have learnt to take components of vectors. But that would require the knowledge of the phase angle as well.
We can use complex numbers here. We can assume the x axis as the real axis and the y axis as the imaginary axis .
Now we need to convert the capacitative reactance(Xc) into resistance
Xc= 1/cw
converting this into resistance we get 1/icw (where i= root(-1) )
1/icw = -i/cw (multiplying and dividing by i)
Inductive reactance ,XL= Lw
converting into resistance we get iLw
and resistance which is already along the x axis can be simply written as R
Example (we use a simple series circuit)
Now the complex number for total impedance,z = R+ iLw - i/cw
=R + i ( Lw -1/cw)
Impedance = mod of z = |z| = root (R^2 + (lw-1/cw)^2 )
and for the phase angle we have arg (z) = tan (phi) = img part/real part = [Lw-1/cw] / R
Now for a complex circuit we can simply add the different components as we would with resistance.
example : if we had a parellel circuit with inductor, resistor and inductor in parellel we would have 1/z = 1/R + 1/iLw - cw/i
(we get this from 1/R= 1/R1 + 1/R2 + 1/R3 ........)
