1、3.5 Analysis of AC Circuits 3.5.1 Calculation of Current and Voltage in AC Circuits The impedance of the resistor, inductor and capacitor of AC circuits are R=RR RVZ I , jLLL LVZ I=, 1jCCC CVZ I= respectively. You may notice that Ohms law applies to AC circuits. Similarly, KCL and KVL also apply to
2、AC circuits. Lets take an example to show the process of calculating current and voltage in AC circuits. Fig. 1 shows an AC circuit with a resistor and an inductor in series. SVILVRV Figure 1: Circuit for example 1. According to KVL and Ohms law, R j L= + = +s R LV V V I I (1) From (1), SR j LSVVI Z
3、=+ (2) The voltage of the resistor is SRR R j L= +RV I V (3) The voltage of the inductor is SjLjL R j L = +LV I V (4) Lets take another example to show the calculating process of AC circuits. Fig. 2 shows an AC circuit with a resistor and a capacitor in parallel. SCIRI 1jC Figure 2: Circuit for exam
4、ple 2. According to KCL and Ohms law, 1j C j CRR= + = + = +SR C S SVI I I V V (5) From above two examples, we can see that the complex operation will be used when analyzing AC circuits. Therefore, the analysis of AC circuits is more complex than the analysis of DC circuits. 3.5.2 Phasor Diagrams Alt
5、hough we can analyze AC circuits through complex operation, it is difficult to distinguish relations among different phasors. A phasor diagram is a convenient and useful tool for geometrically presenting the relationships among the various voltages and currents in an AC circuit. A phasor diagram con
6、sists of a number of straight lines with arrows. Lets start by drawing the phasor diagrams for R, L and C. For a resistor shown in Fig. 3, RRI RV Figure 3: A resistor in AC circuits. R=RRVI (6) The expression (6) shows that the phase difference of the voltage and the current of the resistor is zero.
7、 Thus, we can draw the phasor diagram for the resistor, as shown in Fig. 4. RIRV Figure 4: Phasor diagram for the resistor. For an inductor shown in Fig. 5, jLLI LV Figure 5: An inductor in AC circuits. o90j L L= = LLVI (7) The expression (7) shows that the phase difference of the voltage and the cu
8、rrent of the inductor is 90 degree. Thus, we can draw the phasor diagram for the inductor, as shown in Fig. 6. Note that we choose VL as a reference by selecting its phase angle to be zero. LILV Figure 6: Phasor diagram for the inductor. For a capacitor shown in Fig. 7, 1CjCICV Figure 7: A capacitor
9、 in AC circuits. o1 1 1 90CC jj C C C = = = IV (8) The expression (8) shows that the phase difference of the voltage and the current of the capacitor is 90 degree. Thus, we can draw the phasor diagram for the capacitor, as shown in Fig. 8. CICV Figure 8: Phasor diagram for the capacitor. If there is
10、 more than one circuit element in an AC circuit, we can also draw the phasor diagram. For example, the phasor diagram for the circuit in Fig. 1 is shown in Fig. 9. Note that we choose I as a reference in the series circuit for convenience. ILVSR Figure 9: Phasor diagram for the circuit in Fig. 1. Th
11、e phasor diagram for the circuit in Fig. 2 is shown in Fig. 10. Note that we choose Vs as a reference in the parallel circuit for convenience. ISVRCI Figure 10: Phasor diagram for the circuit in Fig. 2. From the phasor diagrams drawn above, we can clearly see the relationships among the various voltages and currents in an AC circuit from a geometric point of view.
