fra02 New Page 1

 

Strengthening Skills   Building Confidence

 

 

 

 

Procedure

figac1002.gif (1592 bytes)

This figure represents two impedances connected in series with an ac voltage source.

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

ZT = Z1 + Z2

Since this is a summation operation, the impedances are shown in rectangular form. The next step, however, uses ZT in a division operation, so you should convert it to polar form as part of this step.

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

equac1001.gif (963 bytes)

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

IZ1 = IT
IZ2 = IT

Step 4--Use Ohm's law to determine the voltage drops across Z1 and Z2:

VZ1 = IZ1Z1
VZ2 = IZ2Z2

This completes the basic analysis of this ac circuit.

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

VZ1 + VZ2 = VT

Example

Given: Z1 = 500 W, Z2 = 1020 W, VT = 12 V
Find: ZT, IT ,VZ1, and VZ2

Solution:

Step 1--Determine the total impedance of the circuit

Z1 = 500 W = 50 +j0 W
Z2 = 1020 W = 9.4 +j3.42 W

ZT = Z1 + Z2
ZT = 50 +j0 +  9.4 +j3.42
ZT = 59.4 +j3.42 W
ZT =59.53.3 W

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

IT = 120 / 59.53.3
IT = 0.20-3.3 A

Step 3--Determine the currents for Z1 and Z2

IZ1 = 0.20-3.3 A
IZ2 = 0.20-3.3 A

Step 4--Use Ohm's law to determine the voltage drops across Z1 and Z2

VZ1 = (0.20-3.3)(500)
VZ1 = 10-3.3 V


VZ2 = (0.20-3.3)(1020)
VZ2 = 216.7 V

Check

VZ1 = 10-3.3 = 9.98 -j0.58
VZ2 = 216.7 = 1.92 +j0.57
(9.98 -j0.58) + (1.92 +j0.57) = 11.9 -j0.01

(close enough to VT = 12 +j0 V)

David L. Heiserman, Editor

Copyright   SweetHaven Publishing Services
All Rights Reserved

Revised: June 06, 2015