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:
Simple case:
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:
Example 1
Find the combined impedance of the following circuit:
Example 2
Given that Z1= 200 − 40j Ω and Z2= 60 + 130j Ω,
find
a) the total impedance
b) the phase angle
c) the total line current
Example 3
A 100 Ω resistor, a 0.0200 H inductor and a 1.20 µF capacitor are connected in parallel with a circuit made up of a 110 Ω resistor in series with a 2.40 µF 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.
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