Another way to find the complex impedance here would be to actually build the cir-cuit, connect a signal generator to it, and measure R and X directly with an impedancebridge. Because “the proof of the pudding is in the eating,” a performance test musteventually be done anyway, no matter how sophisticated the design theory. Engineershave to build things that work!Ohm’s law for ac circuitsOhm’s Law for a dc circuit is a simple relationship among three variables: current (I),voltage (E), and resistance (R). The formulas, again, areIE/REIRRE/IIn ac circuits containing negligible or zero reactance, these same formulas apply, as longas you are sure that you use the effective current and voltage.Effective amplitudesThe effective value for an ac sine wave is the root-mean-square, or rms, value. Youlearned about this in chapter 9. The rms current or voltage is 0.707 times the peak am-plitude. Conversely, the peak value is 1.414 times the rms value.If you’re told that an ac voltage is 35 V, or that an ac current is 570 mA, it is gener-ally understood that this refers to a sine-wave rms level, unless otherwise specified.Purely resistive impedancesWhen the impedance in an ac circuit is such that the reactance X has a negligible effect,and that practically all of the current and voltage exists through and across a resistanceR, Ohm’s Law for an ac circuit is expressed asIE/ZEIZZE/Iwhere Z is essentially equal to R, and the values I and E are rms current and voltage.Complex impedancesWhen determining the relationship among current, voltage and resistance in an ac cir-cuit with resistance and reactance that are both significant, things get interesting.Recall the formula for absolute-value impedance in a series RLC circuit,Z2R2 X2so Z is equal to the square root of R2 X2 . This is the length of the vector RjX in thecomplex impedance plane. You learned this in chapter 15. This formula applies only forseries RLC circuits.298 RLC circuit analysis