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Strengthening Skills   Building Confidence

 

 

 

 

Procedure

figac1003.gif (1736 bytes)

This figure represents two impedances connected in parallel  with an ac voltage source. The impedances can be purely resistive, capacitive, inductive, or any combination of resistance and reactance.

Step 1--Determine the total impedance of the circuit.  This is a parallel circuit, so:

ZT = Z1 || Z2

 

Step 2--Use Ohm's law to determine the total current:

equac1001.gif (963 bytes)

Step 3--Determine the voltages for Z1 and Z2. These impedances are connected in parallel with the source voltage, so it follows that the voltages are going to be equal to the source, or total, voltage:

VZ1 = VT
VZ2 = VT

Step 4--Use Ohm's law to determine the currents through Z1 and Z2:

IZ1 = VZ1 / Z1
IZ2 = VZ2 / Z2

This completes the basic analysis of this ac circuit.

To check your results, convert the currents from Step 4 into rectangular form and show that:

IZ1 + IZ2 = IT

Example

Given: Z1 = 2040 W, Z2 = 10-90 W, VT = 12 V
Find: ZT, IT ,IZ1, and IZ2

Solution:

Step 1--Determine the total impedance of the circuit

Z1 = 2040 W = 15.3 +j12.9 W
Z2 = 10-90 W = 0 -j10 W

ZT = Z1Z2/Z1 + Z2
ZT = 2040 x 10-90 / 15.3 +j12.9 + 0 -j10
ZT = 200130/15.7 +j2.9 = 200130/16 10.5
ZT = 12.5120

Step 2--Use Ohm's law to determine the total current

IT = 120 / 12.530
IT = 0.96-30
IT = 0.83 -j0.48

Step 3--Determine the voltages for Z1 and Z2.

VZ1 = VT = 12v
VZ2 = VT = 12v

Step 4--Use Ohm's law to determine the currents through Z1 and Z2:

IZ1 = VZ1 / Z1
IZ1 = 120 / 500
IZ1 = 0.24-50

IZ2 = VZ2 / Z2
IZ2 = 120 /10-90
IZ2 = 1.290

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015