can be considered as two forces acting at right angles to each  other. Thus, the relation between resistance, reactance, and  impedance may be illustrated by a right triangle.  [Figure 9-24] Since these quantities may be related to the sides of a right  triangle, the formula for finding the impedance can be found  using the Pythagorean Theorem. It states that the square of  the hypotenuse is equal to the sum of the squares of the other  two sides. Thus, the value of any side of a right triangle can  be found if the other two sides are known.  In practical terms, if a series AC circuit contains resistance  and inductance, as shown in  Figure 9-25 , the relation between  the sides can be stated as: The square root of both sides of the equation gives: This formula can be used to determine the impedance when  the values of inductive reactance and resistance are known. It  can be modified to solve for impedance in circuits containing  capacitive reactance and resistance by substituting X$_{C}$ in the  formula in place of X$_{L}$. In circuits containing resistance with  both inductive and capacitive reactance, the reactances can be  combined; but because their effects in the circuit are exactly  opposite, they are combined by subtraction (the smaller  number is always subtracted from the larger):  coil with an inductance of 0.021 henry. What is the value of  the impedance and the current through the circuit?  Solution: First, the inductive reactance of the coil is computed:  Next, the total impedance is computed: Remember when making calculations for Z always use  inductive reactance not inductance, and use capacitive  reactance, not capacitance. Once impedance is found, the total current can be calculated.  Figure 9-25  shows example 1. Here, a series circuit  containing a resistor and an inductor are connected to a source  of 110 volts at 60 cycles per second. The resistive element is  a simple measuring 6 ohms, and the inductive element is a Since this circuit is resistive and inductive, there is a phase  shift where voltage leads current. Figure 9-24.  Impedance triangle. Figure 9-25.  A circuit containing resistance and inductance. Z =  √  R$^{2}$ + (X$_{L}$ – X$_{C}$)$^{2}$  Z$^{2}$ = R$^{2}$ + (X$_{L}$ – X$_{C}$) 2 Z =  √  R$^{2}$ + X 2 $_{L}$  Z =  √  6$^{2}$ + 8 2 Z =  √ 36 + 64  Z =  √  100 Z = 10Ω  X$_{L}$  = 2π × f × L X$_{L}$ = 6.28 × 60 × 0.021 X$_{L}$ = 8 ohms inductive reactance Z = X$_{L}$ – X$_{C}$ X = X$_{C}$ – X$_{L}$ or  I = E Z I = 110V  10Ω I = 11 amps 110V AC 60 cycles R = 6Ω A X$_{L}$ = 0.021 H Reactance Resistance Z R Impedance X$_{L }$ − X$_{C}$ 9-16