31A - AC Circuits Background In lecture, we deduced the following relationships for AC reactance and the relationship between current and voltage for inductors, capacitors, and resistors. Consider a system in which the current is given by () = 0 cos() and () = 0cos ( ). For all devices - 0 = 0 where X is the Reactance for inductors or capacitors and the Resistance for resistors. The reactance has the same units (ohms) as resistance. For capacitors: = = 1/ and = -/2. For inductors: = = and = /2. For resistors: X = R. When components are wired in series with one another, the current through all components must be the same: = = = , but the voltages will be out of phase with one another. For a resistor R and capacitor C wired in series with current () = 0 cos(), the relationship between ac potential and ac current is: = 0 and = 0 and = ( 2 2 ) = 0(2 2 ) . For an inductor and resistor in series the equations are the same, substituting L for C in the subscripts. (Note that the reactances have different frequency dependence.)