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 Strengthening Skills •  Building Confidence

 Procedure 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: 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 = 50Ð0° W, Z2 = 10Ð20° W, VT = 12 V Find: ZT, IT ,VZ1, and VZ2 Solution: Step 1--Determine the total impedance of the circuit Z1 = 50Ð0° W = 50 +j0 W Z2 = 10Ð20° W = 9.4 +j3.42 W ZT = Z1 + Z2 ZT = 50 +j0 +  9.4 +j3.42 ZT = 59.4 +j3.42 W ZT =59.5Ð3.3° W Step 2--Use Ohm's law to determine the total current IT = 12Ð0° / 59.5Ð3.3° IT = 0.20Ð-3.3° A Step 3--Determine the currents for Z1 and Z2 IZ1 = 0.20Ð-3.3° A IZ2 = 0.20Ð-3.3° A Step 4--Use Ohm's law to determine the voltage drops across Z1 and Z2 VZ1 = (0.20Ð-3.3°)(50Ð0°) VZ1 = 10Ð-3.3° V VZ2 = (0.20Ð-3.3°)(10Ð20°) VZ2 = 2Ð16.7° V Check VZ1 = 10Ð-3.3° = 9.98 -j0.58 VZ2 = 2Ð16.7° = 1.92 +j0.57 (9.98 -j0.58) + (1.92 +j0.57) = 11.9 -j0.01 (close enough to VT = 12 +j0 V)