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 Strengthening Skills •  Building Confidence

 Procedure 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: 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 = 20Ð40° W, Z2 = 10Ð-90° W, VT = 12 V Find: ZT, IT ,IZ1, and IZ2 Solution: Step 1--Determine the total impedance of the circuit Z1 = 20Ð40° W = 15.3 +j12.9 W Z2 = 10Ð-90° W = 0 -j10 W ZT = Z1Z2/Z1 + Z2 ZT = 20Ð40° x 10Ð-90° / 15.3 +j12.9 + 0 -j10 ZT = 200Ð130°/15.7 +j2.9 = 200Ð130°/16 Ð10.5° ZT = 12.5Ð120° Step 2--Use Ohm's law to determine the total current IT = 12Ð0° / 12.5Ð30° IT = 0.96Ð-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 = 12Ð0° / 50Ð0° IZ1 = 0.24Ð-50° IZ2 = VZ2 / Z2 IZ2 = 12Ð0° /10Ð-90° IZ2 = 1.2Ð90°