12. Parallel AC Circuits
Recall Ohm's law for pure resistances:
`V = IR`
In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (`Ω`).
In this case, Ohm's Law becomes:
V = IZ.
Recall also, if we have several resistors (R1, R2, R3, R4, …) connected in parallel, then the total resistance RT, is given by:
In the case of AC circuits, this becomes:
If we have 2 impedances Z1 and Z2, connected in parallel, then the total resistance ZT, is given by
We can write this as:
Finding the reciprocal of both sides gives us:
Find the combined impedance of the following circuit:
Given that Z1= 200 − 40j Ω and Z2= 60 + 130j Ω,
a) the total impedance
b) the phase angle
c) the total line current
A `100\ Ω` resistor, a `0.0200\ "H"` inductor and a `1.20\ mu"F"` capacitor are connected in parallel with a circuit made up of a `110\ Ω` resistor in series with a `2.40\ mu"F"` capacitor. A supply of `150\ "V"`, `60\ "Hz"` is connected to the circuit.
Calculate the total current taken from the supply and its phase angle.