Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important.

#### Impedance

No circuit is without some resistance, whether desired or not. Resistive and reactive components in an AC circuit oppose current flow. The total opposition to current flow in a circuit depends on its resistance, its reactance, and the phase relationships between them.

**Impedance** is defined as the total opposition to current flow in a circuit.

The below Equation is the mathematical representation for the magnitude of impedance in an AC circuit.

where

Z = impedance (Ω)

R = resistance (Ω)

X = net reactance (Ω)

The relationship between resistance, reactance, and impedance is shown in Figure 5.

Figure 5 : Relationship Between Resistance, Reactance, and Impedance

The current through a certain resistance is always in phase with the applied voltage. Resistance is shown on the zero axis. The current through an inductor lags applied voltage by 90°; inductive reactance is shown along the 90° axis. Current through a capacitor leads applied voltage by 90°; capacitive reactance is shown along the -90° axis. Net reactance in an AC circuit is the difference between inductive and capacitive reactance.

The below Equation is the mathematical representation for the calculation of net reactance when X_{L} is greater than X_{C}.

**X = X _{L} – X_{C}**

where

X = net reactance (Ω)

X_{L} = inductive reactance (Ω)

X_{C} = capacitive reactance (Ω)

The below Equation is the mathematical representation for the calculation of net reactance when X_{C} is greater than X_{L}.

**X = X _{C} – X_{L}**

Impedance is the vector sum of the resistance and net reactance (X) in a circuit, as shown in Figure 5. The angle θ is the phase angle and gives the phase relationship between the applied voltage and the current. Impedance in an AC circuit corresponds to the resistance of a DC circuit. The voltage drop across an AC circuit element equals the current times the impedance.

The below Equation is the mathematical representation of the voltage drop across an AC circuit.

**V = IZ**

where

V = voltage drop (V)

I = current (A)

Z = impedance (Ω)

The phase angle θ gives the phase relationship between current and the voltage.