Chapter 25: Parallel AC Networks
Date: 17-6-2019 [cite: 1009]
25.3 Parallel AC Networks
The potential difference across each impedance is the same, and it is equal to the supply voltage. [cite: 1012, 1013, 1014, 1015]
I = I1 + I2 + I3 [cite: 1021]
If ZT is the total impedance, then: [cite: 1023, 1024]
1 / ZT = 1 / Z1 + 1 / Z2 + 1 / Z3 [cite: 1025]
In general for impedances connected in parallel, the total admittance YT is given by: [cite: 1018, 1026]
YT = Y1 + Y2 + Y3 + … + Yn [cite: 1027]
Admittance has its greatest advantage in general circuit analysis. [cite: 1028]
For Two Impedances Connected in Parallel
When there are two impedances connected in parallel, the total impedance ZT is: [cite: 1029]
ZT = (Z1Z2) / (Z1 + Z2) [cite: 1030]
The voltages are represented as V = I1Z1 and V = I2Z2. [cite: 1031]
Some Useful Current Equations
Below are some useful current equations derived from the parallel networks: [cite: 1032, 1033]
V = I ZT = I((Z1Z2) / (Z1 + Z2)) [cite: 1033]
I1Z1 = I((Z1Z2) / (Z1 + Z2)) [cite: 1033]
I1 = I(Z2 / (Z1 + Z2)) = V / Z1 [cite: 1035]
I2 = I(Z1 / (Z1 + Z2)) = V / Z2 [cite: 1033]
I1Z1 = I((Z1Z2) / (Z1 + Z2)) [cite: 1033]
I1 = I(Z2 / (Z1 + Z2)) = V / Z1 [cite: 1035]
I2 = I(Z1 / (Z1 + Z2)) = V / Z2 [cite: 1033]