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: Z_{T} = Z_{1} || Z_{2} **Step 2**--Use Ohm's law to determine the total current: **Step 3**--Determine the voltages for Z_{1} and Z_{2}. 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: V_{Z1} = V_{T} V_{Z2} = V_{T} **Step 4**--Use Ohm's law to determine the currents through Z_{1} and Z_{2}: I_{Z1} = V_{Z1} / Z_{1} I_{Z2} = V_{Z2} / Z_{2} 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: I_{Z1} + I_{Z2} = I_{T} | Example Given: Z_{1} = 20Ð40° W, Z_{2} = 10Ð-90° W, V_{T} = 12 V Find: Z_{T}, I_{T} ,I_{Z1}, and I_{Z2} Solution: **Step 1**--Determine the total impedance of the circuit Z_{1} = 20Ð40° W = 15.3 +j12.9 W Z_{2} = 10Ð-90° W = 0 -j10 W Z_{T} = Z_{1}Z_{2}/Z_{1} + Z_{2} Z_{T} = 20Ð40° x 10Ð-90° / 15.3 +j12.9 + 0 -j10 Z_{T} = 200Ð130°/15.7 +j2.9 = 200Ð130°/16 Ð10.5° **Z**_{T} = 12.5Ð120° **Step 2**--Use Ohm's law to determine the total current I_{T} = 12Ð0° / 12.5Ð30° I_{T} = 0.96Ð-30° I_{T} = 0.83 -j0.48 **Step 3**--Determine the voltages for Z_{1} and Z_{2}. V_{Z1} = V_{T} = 12v V_{Z2} = V_{T} = 12v **Step 4**--Use Ohm's law to determine the currents through Z_{1} and Z_{2}: I_{Z1} = V_{Z1} / Z_{1} I_{Z1} = 12Ð0° / 50Ð0°_{ }I_{Z1} = 0.24Ð-50° I_{Z2} = V_{Z2} / Z_{2 }I_{Z2} = 12Ð0° /10Ð-90° I_{Z2} = 1.2Ð90° |