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Introduction to Electronics, 6th Ed, Eric Gates AC AC Measurements Resistive AC Circuits Capacitive AC Circuits Inductive AC Circuits Resonance Circuits

Two types of electricity

Direct current (DC)
Alternating current (AC)

AC generator

Converts mechanical energy into electrical energy.

Electromagnetic Induction

The process of inducing a voltage in a conductor by passing it through a magnetic field.

Maximum voltage is induced when...

the conductor is moved perpendicular to the lines of flux.

When the conductor is moved PARALLEL to the lines of flux...

NO voltage is induced.


One revolution of an AC generator.
(Also, two complete alternations of voltage with NO reference to time.)


the two halves of an AC cycle. (one positive & one negative)

Hertz (Hz)

One cycle per second.

Major parts of an AC generator

Slip Rings

AC generator output

Sinusoidal wave form (Sine wave)

Sine wave values (pair of numbers)

Degree of rotation- armature's position in the field.
Amplitude-value in relation to maximum or minimum.

Peak value

Absolute value (no negative numbers) of the point of greatest magnitude. (The peak of the curve-positive or negative)

Peak to Peak

Max positive to Max negative. (Add the absolute values)

Effective value

The amount that produces the same degree of heat in a given resistance as an equal amount of DC.

RMS value

Root Mean Square - same as effective value. Is calculated mathematically.

What value does a multimeter measure?

RMS value. (effective value)

Formula for RMS value

E rms = Ep X .707


The time required to complete one cycle. Measured in seconds.


The number of cycles that occurs in a specific period of time.
(Usually cycles per second)

The unit of frequency is

the hertz

The period of a sine wave is

inversely proportional to its frequency. (higher freq-lower period)

Frequency-period formula

f= 1/t

Nonsinusoidal waveforms

Other than sine wave.
Square, triangular, saw tooth

Pulse width

(Square wave) The duration that the voltage is at the max or min amplitude. Pulse width is one half of the period-hence square.

Triangular wave

Linear rise in value. Positive and negative ramps of equal slope.

Saw tooth wave

(Special triangular wave) Long, linear positive ramp with rapid negative ramp

Fundamental Frequency

The repetition rate of the waveform


Higher frequency sine waves that are exact multiples of the fundamental frequency.

Square wave harmonics

Fundamental frequency and all ODD harmonics

Triangular wave harmonics

Fundamental frequency and all ODD harmonics AND all are 180 degrees out of phase.

Sawtooth wave harmonics

ODD and EVEN harmonics. Even are 180 degrees out of phase with odd.

Moving Coil Meter

d'Arsonval meter movement

Moving coil meters are designed to measure..

DC current

How is AC current measured with a moving coil meter?

The AC current must first be converted to DC.


The process of converting AC current to DC. Accomplished with diodes.

Rectifier output

pulsating DC (sine wave is flipped to all positive alternations)

Clamp on ammeter

A split core transformer. It is clamped around the conductor and uses the voltage induced by the conductors magnetic field

Oscilloscope provides the following data:

Phase relationship (of 2 or more waveforms)
Shape of a waveform

Parts of an oscilloscope:

Cathode Ray Tube
Sweep generator
Horizontal deflection amp
Vertical deflection amp
Power supply

Iron vane meter movement does not require

conversion to DC

In phase

Phase relationship such that current and voltage pass through peaks and zeros at the same time.

In Phase relationship

Purely resistive circuits are

IN PHASE. Voltage and current pass through max and zero at the same point.

Current is always ____ in a resistive circuit

In phase with voltage.

Power in a resistive AC circuit. Power is always positive.

Most widely used measurement value for AC

Effective (RMS) value

Does current flow across a capacitor?

NO! The capacitor charging and discharging results in movement of electrons from one plate to the other. This resembles current flow.

Capacitive AC circuit - I >C>E

Capacitive reactance formula

Capacitive Reactance

The opposition that a capacitor offers to the applied AC voltage.


Current (I) leads Voltage(E) in a capacitive circuit (C)
I>C>E (Remember ELI the ICE man.)

Capacitive Circuit Operation

Voltage starts from zero. Capacitor is empty. Current becomes max. Capacitor charges. Current drops as voltage becomes max and capacitor nears full charge. At max voltage capacitor is fully charged & current drops to zero. Voltage drops towards negative. Capacitor opposes and negative current flows as capacitor discharges.

Capacitive Reactance in Parallel

1/XCT = 1/XC1 + 1/XC2 + 1/XC3 ... + 1/XCn

Capacitive Reactance in Series

XCT = XC1 + XC2 + XC3 ... + XCn

RC Low Pass Filter

RC Low Pass Operation

Allows low frequencies to pass while attenuating high frequency. At low frequency, capacitive reactance is HIGH so voltage drop is across capacitor.

RC High Pass Filter

RC High Pass Operation

Allows high frequency to pass while attenuating low.
At high frequency, capacitive reactance is LOW so voltage drop is across the resistor.

Low Pass Frequency Response

High Pass Frequency Response

Decoupling Network

Allows a DC signal to pass while blocking the AC signal.

What type of circuit can be used as a decoupling network?

RC low-pass filter.

Coupling Network

Passes the AC signal while blocking the DC

What type of circuit can be used as a coupling network?

An RC high-pass filter


A circuit that discriminates against certain frequencies.

RC circuit uses

Filtering (low/high pass)
Coupling(and decoupling)
Phase shifting

RC phase shift networks are used only where

small amounts (less than 60 degrees) are desired.

RC leading output phase-shift network

Inductive Reactance

The opposition to current flow by an inductor in an AC circuit.

Counter Electromotive Force (CEMF)

Voltage induced in an inductor coil which opposes the applied voltage. It is out of phase by 180 degrees.

Factors effecting CEMF

The greater the rate of change of the magnetic field (faster the magnetic field expands or collapses) the greater the CEMF.


Voltage (E) leads Current (I) in an inductive (L) circuit

Inductive Reactance Formula

Impedance Formula

Decoupling Network - Memory Trick

D-coupling = d C pass

Coupling Network - Memory Trick

C-oupling = a C pass

RC Low pass filter - Memory Trick

Capacitor low = frequency low
(Capacitor low in schematic. Low frequency passes)

RC High pass filter - Memory Trick

Capacitor high=frequency high
(Capacitor high in schematic. High frequency passes)

Leading Output Phase-Shift Network
Memory Trick

Look for C. (C slows voltage) C in back - input slow-output leads. Output voltage leads input voltage.

Lagging Output Phase-Shift Network
Memory Trick

Look for C. (C slows voltage) C in front-output slow-input leads. Output voltage lags input voltage.


The combined effect of resistive and reactive components.
It is the vector sum.

Why is the capacitive voltage vector (Ec) drawn downward?

It lags current by 90 degrees. This is why it points down (-90 degrees).

Why are current vectors used to analyze a PARALLEL circuit?

Because the VOLTAGE is the SAME across all components.
All are EQUAL and IN PHASE with current, so that vector is the horizontal (X) axis.

Why are voltage vectors used to analyze a SERIES circuit?

Because the CURRENT is the SAME across all components.
All are EQUAL and IN PHASE with voltage, so that vector is the horizontal (X) axis.

Power Factor

The ratio of true power (in watts) to apparent power (in volt-amperes) in a REACTIVE circuit.

Power factor of RESISTIVE circuit

True power EQUALS apparent power so power factor is 1.

The value of capacitive reactance _______ as frequency increases

decreases (inversely proportional)
High freq=low Xc

What is the formula for cutoff frequency in an RC circuit?

Counter electromotive force (cemf)

Voltage induced in an inductor coil by the expansion and collapse of the magnetic field resulting from an applied voltage.

CEMF characteristics

Always opposes applied voltage.
Greater inductance=greater cemf
Always 180 degrees out of phase with applied voltage.

Induced voltage is always _____ than applied voltage


In a purely inductive circuit current ___ voltage.

LAGS - remember ELI the ICE man.
E(voltage) L(inductive circuit) I(current)
Current lags by 90 degrees.

The opposition to current flow by an inductor in an AC circuit is

inductive reactance (Xl) measured in ohms

Inductive reactance formula

Inductive reactances in series

When inductors are connected in series, the total inductive reactance is equal to the sum of the individual inductive reactance values

Formula for inductive reactance in series

Formula for inductive reactances in parallel

RL Low pass filter

RL High pass filter

RL cutoff frequency formula

RL Circuit Vector Formula

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