### Table of Contents

# Electrical Impedance

Electrical Impedance is defined as being anything which causes an opposition to current flow within a circuit. This often confuses newcomers to electrical science somewhat, because we usually think of resistance as being defined as the opposition to current flow, but in actual fact resistance is just one component of impedance in an AC circuit, albeit the most common one. The other two components of impedance are inductive reactance and capacitive reactance.

Inductive reactance is caused by inductive loads, the most common examples of which are the inductive motor or the simple coil of wire.

Capacitive reactance is caused by capacitive loads, or capacitors.

Both types of reactance cause opposition to current flow as a result of current and voltage becoming ‘out of phase’. In a capacitive circuit the current leads the voltage, whereas in an inductive circuit the voltage leads the current. This simply means that the current and voltage are out of sync, with the sine wave representing the current either leading or lagging that of the voltage when plotted over time.

Resistance can be defined more specifically, and hence accurately than the common definition, by saying that it represents the physical resistance of the conducting material to current flow. A purely resistive circuit with no reactance is said to be ‘in phase’, because the current and voltage are in sync with each other.

## Basic Impedance Formulae

### Inductive Reactance

XL = 2 * pi * f * l, where:

XL = Inductive reactance

F = frequency

L = Inductive load (measured in Henrys)

Remember: Come to the induction and get 2 pies for lunch!

### Capacitive Reactance

XC = 1 / 2 * pi * f * c, where:

XC = Capacitive reactance

F = Frequency

C = capacitive load (measured in Farads),

Remember: One person per 2 pies for church!

### Total Reactance

Inductance and capacitance cancel each other out, so in circuits containing both the total reactance is calculated simply by taking the smaller figure away from the larger figure.

### Total Impendence

Z = the square root of (R squared + X squared), where:

Z = Impedance

R = Resistance

X = Total reactance

This is derived from the Pythagorean Theorem.

## Impedance and Power Factor

Whereas the resistance of a circuit is a fixed constant which cannot be changed without remaking the whole circuit with a different material or in a different size, the reactance of a circuit can be change to reduce opposition to current flow and therefore make the circuit more efficient.

The efficiency of a circuit is represented in this context by its ‘power factor’. A power factor of 1 is called ‘unity’ and represents a purely resistive circuit with no reactance. As the power factor recedes from 1 towards 0 the circuit becomes less efficient due to increased reactance. This means that more current must be drawn to do the same amount of work.

This can be corrected by introducing a capacitive load to an inductive circuit, or vice versa, which is commonly done in circuits involving inductive motors or florescent lighting which both require capacitors to improve efficiency.

### Power Factor Formulae

Power factor is defined as the cosine of the phase angle between voltage and current, and this is the first of three ways that it can be calculated. The other two are:

1) P.F. = True Power / Apparent Power, where:

P.F. = Power Factor

True Power = the actual power output achieved (Watts)

Apparent Power = in practical terms, the rated power of the device, or the power which would be achieved if there were no reactance (KVA – Kilovolt Amperes).

2) P.F. = R / Z, where:

R = Resistance

Z = Total impedance

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