In ac circuits with resistance alone, the circuit is analyzed the same way as dc circuits, generally with rms ac values. Without any reactance, the phase angle between V and I is zero.
When capacitive reactances alone are combined, the XC values are added in series and combined by the reciprocal formula in parallel, just like ohms of resistance. Similarly, ohms of XL alone can be added in series or combined by the reciprocal formula in parallel, just like ohms of resistance.
Since XC and XL are opposite reactances, they offset each other. In series, ohms of XC and XL can be subtracted. In parallel, the capacitive and inductive branch currents IC and IL can be subtracted.
In ac circuits, R, XL, and XC can be reduced to one equivalent resistance and one net reactance.
In series, the total R and net X at 90° are combined as <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072988215/363997/23_05sum.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>. The phase angle of the series R and X is the angle with tangent ±X/R. To find I, first we calculate ZT and then divide into VT. For parallel branches, the total IR and net reactive IX at 90° are combined as <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072988215/363997/23_06sum.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> The phase angle of the parallel R and X is the angle with tangent ±Ix/IR. To find ZEQ first we calculate ZT and then divide into VA.
The quantities R, XL, XC, and Z in ac circuits all are ohms of opposition. The differences with respect to frequency and phase angle are summarized in Table 23–1.
The phase relations for resistance and reactance are summarized in Fig. 23–15. In ac circuits with reactance, the real power P in watts equals I2R, or VI cos 0, where 0 is the phase angle. The real power is the power dissipated as heat in resistance. Cos 0 is the power factor of the circuit.
