FIGURE 16-16The "phase meter" shows the effect of frequenc! on the phase angle of a circuit, The"phase meter" indicates the phase angle change between two voltages, V, and Vp. Since Vpand I are in phase, this angle is the same as the angle between V, and LFigure 16-17 uses the impedancetriangle to illustrate the variations inX6, Z, and 0as the frequency changes. Of course, R remains constant. The key point is that because X6'varies inversely with the frequency, so also do the magnitude of the total impedance andthe phase angle. Example 16-4 illustrates this.vrl7 fflGURE16-17As the frequency increases, Xg decreases, Z decreases, and0 ilecreases. Each value of frequency can be visualized asforming a dffirent impedance triangle.Increasing /ftLc3^c2J 2J 1Phase meterPhase meter^cl
610 r RC CIRCUITSSECTION 1 6-3 1. In a certain series RC circuit, Vn = 4 V, and Vc = 6 V. What is the magnitude of theREVIEW source voltage?2. In Question 1, what is the phase angle between the source voltage and the current?3. What is the phase difference between the capacitor voltage aad the resistor voltagein a series RC circuit?4. When the frequency of the applied voltage in a series RC circuit is increased, whathappens to the capacitive reactance? what happens to the magnitude of the totalimpedance? What happens to the phase angle?EXAMPLE 16-4For the series RC circuit in Figure 16-18, determine the magnitude of the total imped-ance and the phase angle for each of the following values of input frequency:(a) 10 kHz (b) 20 kHz (c) 30 kHzFIGURE 16-18Solution(a) For/= 10kHz,_ _ | I= 1.59 kQ2nfC 2n(r0kHz)(Q.01 pF)0.01 pFz=f R\ x/z-tan-'lIt\- \ R /= @z-t"''(ffi) = r.ssr-sz.e. koThus, Z= 1.88 kO and 0 = -57.9'.(b) Forf=20kHz,"'=;rzo **0o' uo, = 7e6 r2z = @ Lan-, (J9SP) = r.zz.-zs.s. koThus, Z = 1.28 kO and 0 = -38.5'.(c) For/= 30 kHz,x'= t(30 kHhJl ,F) = 531 oz = @.2-tan-r(!11 I \ = t.tzt-zs.o" koThus, Z= 1.13 kO and 0 = -28.0".Notice that as the frequency increases, X6, Z, and d decrease.Related Prohlem Find the magnitude of the total impedance and the phase angle inFigure 16-18 for f = | kJlz.I coverage of serics reuctive circuits continues in chapter 17, Part r, on page 664.
r IMPEDANCE AND PHASE ANGTE OF PARATTEL RC CIRCUITSIn this section, you will learn how to determine the impedance and phase angle of aparallel RC circait. Also, capacitive susceptance and admittance of a parallel RC cir-cuit are introduced,After compkting this section, you should be able toI Determine impedance and phase angle in a parallel RC circuit. Express total impedance in complex form. Define and calculate conductance, capacitive susceptance, and admittanceFigure l6-19 shows a basic parallel RC circuit connected to an ac voltage source.FIGURE 16-19Basic parallel RC circuit.The expressionfor the total impedance is developed as follows, using the rules ofphasor algebra. Since there are only two components, the total impedance can be foundfrom the product-over-sum rule.z (R/0")dcz-90")t = R a x ,By multiplying the magnitudes, adding the angles in the numerator, and converting thedenominator to polar form, we getRxcl(o" - 90')Z -\/n\x'rz.-- (+)611