Alternating Current

Alternating current originated with the accumulation of discoveries made in the 19th century by the electrical pioneers that developed the generator.  The speed of the rotary motion of the generator armature cutting through a force field provides the frequency of the AC current and the use of algebra and trigonometry provides a means to calculate the the generators output voltage and power.  

Unlike Direct Current, where current flows in one direction only, Alternating Current reverses its direction of current flow every half cycle of armature rotation. Also, the voltage polarity reverses with each half cycle of the generator coil.

 

Important definitions:

Frequency – The number of complete revolutions the generators armature turns in one second.  Household voltage in the U.S. operates at a frequency of 60 Hertz. (60 cycles per second).  Therefore it requires 1/60th of a second to generate one cycle.

Period – The time required to turn the generators armature one complete revolution (360 degrees).  The period of household voltage is 16.6 milliseconds.  (1 / 60 =  0.0166)

Alternation – Each half cycle of an alternating voltage is called an alternation.  (An alternation is equal to ½ the period.

Amplitude - Household voltage is usually set at 120 volts by the power company supplying the electricity.  The kitchen and utility room have a 240 volt outlet for the range and clothes dryer. Household AC voltage ratings are presented in terms of effective value; that is, it is the voltage that will cause the same amount of heat to be produced in a resistive circuit that is produced by a direct current or voltage of the same value.

Peak Voltage:  The peak value of the 120 volt household voltage is 1.414 times the effective value (120 X 1.414 = 169.68 volts).  Oscilloscopes display the peak values of a waveform plotted over a time period.

Peak to Peak Voltage:  The peak to peak value of a 120 volt line will be twice the peak voltage. 169.68 X 2 = 338.36 vac.

Effective Value:  Hand held voltmeters generally display voltage measurements in "effective values". Another measurement term for "effective value that is frequently used is called the "RMS' value, (Root Mean Square). If you know the peak value and want to find the effective value, multiply the peak value by 0.707.  (169.68 X 0.707 = 120 volts rms).

Resistance

Resistance:  In DC circuits, the opposition to current flow is called resistance. Resistance dissipates energy in the form of heat.  Most matter has resistance to the flow of electricity; the resistance is very small in a conductor like copper wire and very high for an insulator like a piece of mica. 

Although copper wire has a very low resistance, in his early electrical transmission system, Edison discovered that the wire that transported DC power economically from his power station to the city of New York was limited to a distance less than 20 miles due to the accumulated resistance of the wire itself. 

Impedance

Impedance:  In AC circuits, resistance is referred to as impedance.  Impedance is the sum of resistance plus reactance values. Resistance in DC circuits can be calculated using Ohm’s law.  Ohm’s law applies to AC circuits too.  In both cases, the ohm is the unit of measure.

If a resistor is the only component in an AC circuit, impedance and resistance of the circuit are the same.  Components called inductors and capacitors add reactance to AC circuits.  Unlike resistors, these components do not dissipate electrical energy as heat, but alternately store energy and then deliver the energy back to the circuit with each cycle.  Impedance takes into account the effects of inductance and capacitance in addition to the resistance in an AC circuit.

 

Wavelength

Wavelength:  The distance between two successive like points on a sine wave. 

Phase:  Phase refers to the time interval occurring between like values.  Where reactive components are included in the circuit, the  waves for current and voltage begin at different time intervals.  The measurement of this difference is called phase shift.

 

 

 

 

 

 

 

 

The above figure shows that current and voltage are out of phase by 90 degrees.

Phase Relation in a Resistive Circuit
Since the sine waves for voltage and current always pass through zero at the same time and in the same direction, current and voltage are always in phase with one another.  The amplitude of the sine waves are not necessarily the same.  Therefore, voltage, current, resistance and power calculations are made the same as for DC circuits.

If the known quantity is the effective value, then the unknown will be the effective value.

Example:  Ieff = Eeff / R       ie: 120V / 50 ohms = 2.4 amps

The voltage in your home is rated in terms of effective value.  120 VAC.  Another term for effective value is RMS value (Root mean square).  The RMS value is the AC voltage or current that will cause the same amount of heat in a resistance as the equivalent DC voltage or current.

When the peak value of the known value is used, the result will be a peak value.

Example:  Ipeak = Epeak / R  ie:  169.68Vpeak / 50 = 3.39 amps

 

Power:  The power in a purely resistive AC circuit can be determined using the same formulas as for DC circuits.
Example: 

• P = E X I     ie:  120V X 2.4 A = 288 Watts
• P = I²R      ie:  (2.4 A)² X 50 ohms = 288 Watts
• P = E²R     ie:  (120 V)² / 50 ohms = 288 Watts

 

Inductance

Inductance is the opposition to a change in current.  It is also referred to as back emf, or counter emf.  In an AC circuit, when an alternating voltage is applied to a coil in the circuit, the magnetic field created by the coil is constantly expanding and collapsing, causing a continuous back emf.  The symbol for inductance is L and the basic unit is the Henry.  A coil has an inductance of one henry when a current variation of one ampere per second induces one volt of counter emf.

Any conductor that carries AC current has some  inductance, however, an inductor is usually a coil of wire.  Factors that affect the amount of inductance in a coil are:

Number of turns of wire
Spacing of the turns
Method of winding the coil
Type of core
Diameter of the coil
Ratio of the diameter to the length of the coil

Three common types of cores for an inductor are the air core, the powdered iron core and the iron core.  The iron core has a greater inductance than the air core because iron has less opposition to the lines of force than air.

When the field of an inductor induces a back emf in the inductor itself, the inductance is called self inductance.  The voltage of self inductance is determined by the inductance of the coil and the rate at which the current changes through the coil.  This voltage is opposite in polarity to the applied voltage (Back emf).

Mutual induction occurs when the magnetic field of one coil cuts across the turns of another coil.  The coils are said to be coupled.  Transformers operate by mutual induction.

 

Phase Relation in a pure inductive circuit.

When an inductor is connected to an AC circuit, the current lags the voltage across the inductor.  In a pure inductive circuit, current lags the voltage by 90 degrees.  Another way to remember – Voltage leads current in an inductive circuit. ELI.  Maximum current flows when voltage crosses zero.  Back e.m.f. always opposes the applied voltage.

 

Inductors connected in series: 

When two or more coils are connected in series, and there is no mutual inductance between them, the total inductance is equal to the sum of the individual inductors.

Expressed as follows:  Lt = L1 + L2 + L3 + L4

 

Inductors connected in parallel:

When two or more inductors are connected in parallel and there is no mutual induction between them, the total inductance is found by taking the reciprocal of the sum of the reciprocals.

Expressed as follows: Lt = 1 / (1/L1 + 1/L2 + 1/L3 + 1/L4)

If only two inductors are connected in parallel, the total inductance may be calculated as follows:  Lt = L1 X L2 / L1 + L2

 

Inductive Reactance

The opposition of an inductor or a coil to the flow of alternating current is called inductive reactance.  The amount of inductive reactance of a coil depends upon the following:

Inductance of the coil
Frequency of the alternating current
The constant 2π = 6.28

The formula for inductive reactance is:

          XL = 2π fL

Where XL is the inductive reactance
f is the frequency of the AC in Hertz
L is the inductance of the coil in henrys

Example:

What is the inductive reactance of a 10 henry coil when the frequency of the AC through the coil is 60 Hertz.

XL = 2π fL  =  6.28 x 60 x 10 = 3768 ohms

It is improbable that you will find an inductor that contains no resistance, the wire it is made from contains some resistance in the wire itself, but to simplify the following exercise, consider the inductor to have negligible resistance. 

1. The voltage in the circuit is 240 VAC.  Find the current in the circuit that is due to the action of the voltage and inductive reactance.

 

I = EL / XL = 240 / 3768 = 0.0636 amps. (63.6 ma)

1. A coil is connected to 120 VAC, 60 Hz.  Current flowing through the coil is 0.75 amps.  What is the inductance of the coil?

 

EL = 120 vac.
f  = 60 Hz.
I =  0.75 amps (750 ma)

Then:  XL = EL / I = 120 / 0.75 = 160 ohms

Since XL = 2πfL

Then L = XL / 2πf = 160 / 6.28 x 60 = 0.424 henrys. (424 mh)

There is a similarity of relationships between voltage and current for inductive reactance and resistance. Both offer an opposition to alternating current, both are expressed in ohms, and both are equal to the voltage divided by current.

 

Power loss in inductors:

All inductors have a certain amount of resistance due to the resistance in the wire used to make the inductor.  This resistance varies with the gauge of wire, the length required, also the type of wire used. The power wasted by the resistance in the wire is called copper loss.  Copper loss may be calculated as follows:  Multiply the square of the current through the coil by the resistance of the winding (I R).  The wire used in the inductor must be large enough to carry the current required by the load to prevent burn out.

Iron core coils have two types of losses, hysteresis loss and eddy current loss:

Hysteresis loss is due to the energy consumed in reversing the direction of the magnetic field of the iron core as the direction of current flow through the winding changes.

Eddy current loss is due to currents that are induced in the iron core by the magnetic fields around the turns of the coil. 

The energy that cannot be returned to the electrical circuit is converted to heat.

 

Series Resistance/Inductance  (RL) Circuits.

In a series AC circuit, the current flow through an inductor and a resistor is the same.  However, the voltage across the resistor is in phase with current and the voltage across the inductor leads the current through the inductor by 90 degrees. 

Kirchoffs second law for DC and AC resistive circuits states that the sum of the voltage drops around a completed circuit equals the applied voltage of the source.  This is also true for AC circuits that contain reactive components, but the voltage must be added vectorially rather than directly.  Phase angle is usually represented by the Greek letter theta ( θ ).

The figure on the right shows a resistor and inductor connected in series across a voltage source.  The figure on the left depicts a vector diagram of the circuit on the right.  EL, Ea and Er are called “vectors”.  A vector indicates both magnitude and direction.  The horizontal line is the current vector, the vertical line represents the voltage across the inductor.  The angle between the current vector and the applied voltage vector is called the phase angle and is less than 90 degrees.

A reactance chart can also be used to determine vector sum and phase angle.  There are programs available on the internet that can calculate these values too.

 

Impedance  in an RL Circuit.

Impedance does not indicate phase and is not a vector quantity, it indicates only “amount”.  However, the total impedance of an RL Circuit can be found in similar fashion using the reactance chart.

 

Power Factor (pf).

In a purely resistive circuit, the power dissipated is equal to E X I  or I² R.  The dissipated power appears in the form of heat.  In a purely inductive circuit, all the power is returned to the  source  when the built up magnetic field collapses; no power is lost as heat.  It is the resistance of the circuit that produces heat.

Apparent Power is the applied voltage times the current in the circuit.

True Power is the power that is actually dissipated in the circuit.

The  Power Factor equals True Power divided by Apparent Power.  This is also the cosine of the phase angle theta in a vector chart.  In terms of using trigonometry for this definition, the power of a reactive circuit is equal to

P = EI cos θ. 

Note:  Power Factor is a number whose minimum value is Zero when the circuit is purely inductive and a maximum value when the circuit is purely resistive.  In an RL circuit, the power factor will be greater than Zero and less than One.

 

Capacitance  in AC circuits.

A resistor has the same effect in both DC and AC circuits.  An inductor stores energy in a magnetic field that changes with the flow of current to return a portion of energy back to the source whenever the magnetic field collapses.  A capacitor is another component that stores energy.

The symbol for capacitance is (C) and the basic unit is the farad (f).  Capacitance can be defined as the property of a circuit that opposes any change in voltage.  A capacitor has the capacitance of one farad when one coulomb of electricity charges it to one volt.  The farad is a rather large unit, so capacitors are typically rated in units of micro-farads or pica-farads. 

Capacitance also denotes the storage of charge.  The Leyden jar invented by Pieter van Musschenbroek in 1745 to store electric charge to generate a spark of static electricity is attributed to be the earliest capacitor. This device consisted of a glass vial partially filled with water and sealed with a cork. A thick conducting wire protruded from the cork. 

An English physicist William Watson quickly developed a more sophisticated version that utilized foil wrapped around the inside and outside of the glass vial.  The stored charge was provided by touching the protruding tip of the conducting wire with a static generator. 

During the last 250 years since the Leyden jar, scientists and engineers working in corporations have developed the capacitor into small and reliable components for use in many electronic applications.

 

Build a capacitor:  You can build a capacitor by taking two strips of aluminum foil (let’s call them plates), perhaps one inch wide by 36 inches long; place a slightly larger strip of waxed paper (the dielectric material) between the aluminum foil strips to insulate them from one another and roll them up tightly, taking care that the aluminum strips never touch each other.  Now the problem becomes keeping it rolled tight and attaching leads to this device so you can attach it to a circuit to store a charge. 

The largest charge you can store will be determined by the breakdown voltage of the insulating material between the two strips of aluminum foil (in this case, it is waxed paper).  The breakdown voltage is a term that states the maximum voltage that can be applied to a capacitor.  Capacitors breakdown due to a short circuit through the insulating material (called the dielectric). Overheating of the device usually degrades the dielectric. The distance between the plates of a capacitor, the type of dielectric material used and the area of the plates all determine the electrical capacitance of the capacitor.  Sounds complicated, doesn’t it.  Electrical components like capacitors are plentiful and easier to purchase from a manufacturer rather than attempt to build them.

When two conductors are separated by an insulator, a capacitor is formed.   As you walk across the rug on a cold dry day, it is the capacitance of your body that stores the static charge that startles you when you touch a metal object, like a door knob or car door.  As a point of interest, I have found that if you hold a small metal object in your hand, such as a key,  touch the door knob with the key first, to discharge the built up charge and you will not be startled, as the spark will jump from the key to the door knob.

 

Voltage and current  relationships in a purely capacitive circuit.

At the first instant when a voltage is applied to a purely capacitive circuit, the current flow will be high and there is no charge on the capacitor.  The next instant, current starts charging the capacitor and voltage starts to oppose the applied voltage. The capacitor will continue to charge until the voltage across the capacitor equals the applied voltage.  In a purely capacitive circuit, current leads voltage by 90 degrees. This means that when current is at maximum, voltage is at minimum and visa versa. 

 

Capacitive reactance

The opposition of a capacitor to the flow of alternating current is called capacitive reactance (Xc).  The amount of capacitive reactance depends on the electrical size of the capacitor, the frequency of the applied AC, and the  constant ½π or .159.    Units of Xc are measured in Ohms.

The formula is as follows:  Xc= 1 / 2π fC

Xc is the capacitive reactance in ohms
f is the frequency of the applied voltage in hertz
C is the capacitance of the capacitor in farads

Capacitive reactance is said to vary inversely with frequency and capacitance.

Example:  Find the capacitive reactance of a .01 microfarad capacitor at a frequency of 60 hertz.   Xc= 1 / 2π fC = 1/ 6.28 x 60 hz x .01 x 10ˉ6

                   Xc  = 1 / 3.768 x 10ˉ6 = 265392 ohms or 265.4 kilo ohms

Note:  .01 x 10ˉ6 microfarad is the same as .01/1000000 

 

Capacitors connected in series

When two or more capacitors are connected in series, the total capacitance is equal to the reciprocal of the sum of the reciprocals of the individual capacitors.

                   Ct = 1/ 1/C1 + 1/C2 + 1/C3

Note: The Value of total capacitance for all the capacitors connected in series will be smaller than the value of the smallest capacitor.

Example:  Find the total capacitance of a circuit containing a 0.5mfd, 0.25mfd and 0.1mfd capacitors connected in series.

                   Ct = 1/1/0.5x10ˉ6 + 1/0.25x10ˉ6 +1/0.1x10ˉ6

Finding the lowest common denominator of the terms in the denominator yields:

                   1 / 1+2+5 / 0.5x10ˉ6 = 1 / 8 /0.5x10ˉ6 =  0.0625x10ˉ6 = .0625mfd

The capacitive reactance of this series circuit can be found in either of two ways:

1. Find the capacitive reactance of each individual capacitor and sum the results

 

Xct = Xc1 + Xc2 + Xc3

1. Use the formula 1 / 2π fC

 

Note: the reciprocal of 2π is 0.159236

                   Xct = 0.159236 / 3.75 x 10ˉ6 = 42463 ohms

 

Capacitors connected in parallel

When two or more capacitors are connected in parallel, the total capacitance is equal to the sum of the individual capacitance’s.

                             Ct = C1 + C2 + C3

Where Ct is the total capacitance, and C1, C2, and C3 are the individual capacitance’s.  Capacitors that are in parallel may be considered as one capacitor with a greater plate area.

Example:  Find the total capacitance of a parallel circuit with a 0.5 mfd, a 0.25 mfd and 0.1 mfd capacitor.

                             Ct = 0.5 + 0.25 + 0.1 = 0.85 mfd or 850 picofarad

The total capacitive reactance of two or more capacitors connected in parallel is equal to the reciprocal of the sum of the reciprocal of the individual capacitive reactances.

                             Xct = 1 / 1 / Xc1 + 1 / Xc2 + 1 / Xc3

For example:  Find the capacitive reactance of the following capacitors connected in parallel that have the values of 0.5 mfd, 0.25 mfd and 0.1 mfd ; the frequency is 60 Hz.

To begin, find the individual capacitive reactance of each capacitor.

                             Xc1 = 0.159 / 60 x 0.5 x 10ˉ6         = 5300 ohms              

                             Xc2 = 0.159 / 60 x 0.25 x 10ˉ6 = 10600 ohms

                             Xc3 = 0.159 / 60 x 0.1 x 10ˉ6 = 26500 0hms

Then:
                   1 / 1 /5300 + 1 / 10500 + 1 / 26500

find the common denominator, in this case 53000 will work.

So:
                   1 / 10 + 5 + 2 / 53000 =3118 ohms

In this case, since you already know that the total capacitance of the circuit is
 0.85 mfd,  the solution can be simplified:

                   Xct = 0.159 / 60 x 0.85 x10ˉ6 = 0.159 / 51 x10ˉ6 = 3118 ohms

 

Power Losses in Capacitors

Some power loss is dissipated in any capacitor, regardless of its construction.  These losses are classified as resistance loss, leakage loss, dielectric absorption loss, and dielectric hysteresis loss.

Resistance losses are caused by the resistance of the plates and connecting wires.
(I²R loss).  These losses represent a very small amount of  the total loss of energy in a capacitor.

Leakage losses are due to the small amount of current that flows through the dielectric material from one plate to another  Air dielectric and mica dielectric have very small leakage losses while other types of dielectric material have considerably more leakage loss.  These losses result in heating of the capacitor.  Excessive heating can degrade the capacitor.

Dielectric absorption loss:  some dielectric such as paraffin impregnated paper, absorb charges as the capacitor is being charged.  These absorbed charges are not given up as the capacitor is discharged and therefore constitute an energy loss.

Dielectric hysteresis loss is similar to the hysteresis loss in the core of inductors.  It requires energy to reverse the polarity of the electric field that exists between the plates of  the  capacitor, the same as it requires energy to reverse the magnetic field in the core of an inductor.  This loss causes heat in an amount determined by the frequency of the alternating voltage across the capacitor.  At low frequencies, this loss is negligible, but is very noticeable at higher radio frequencies.

 

Types of capacitors

Capacitors can be classified into several types according to the dielectric materials used.  They are:  air, paraffin- impregnated paper, mica, ceramic, oil and electrolytic.

Air dielectric capacitors are used in radios for tuning the oscillators in the radio to the correct frequency that  allows the radio circuits to receive the station you want to hear.

Paraffin impregnated-paper dielectric capacitors have a relative dielectric loss at higher frequencies and are commonly found in audio circuits.

Mica dielectric capacitors are used in circuits that carry high radio frequency currents.  Mica has less loss than any of the other common types of capacitor types mentioned.

Ceramic capacitors have most of the desirable qualities of mica capacitors. They can be made with positive or negative temperature coefficient of capacitance.  That is, they can change their capacitance with changes in temperature.

Oil dielectric capacitors can withstand higher voltages than most other types and are found in the utility industry.

Electrolytic capacitors are constructed of aluminum plates that are separated with a chemical in liquid or paste form. A DC voltage is applied across the terminals of this capacitor forming a thin film of insulating oxide on the positive plate.  Since the film dielectric is very thin, this type of capacitor has a large amount of capacitance for a small physical size.  Values rang from 8 mfd to 10000 mfd.  These capacitors are used in DC circuits because a designated plate must always be positive.  They are usually marked to indicate the positive plate.  Reversing the voltage polarity on these capacitors causes them to overheat and sometimes explode.

 

RC Circuits

When a capacitor and a resistor are  connected in a series circuit, the same current flows through both components.  The same is true for an inductor and resistor connected in series.  Electrons do not actually flow through a capacitor as they do through a resistor or coil.  In an AC circuit, due to the charging and discharging of the capacitor, the effect is the same.  In a series circuit, a capacitor can be used to block DC and pass AC.

Voltage developed across a capacitor lags the current by 90 degrees, while the voltage across the resistor is in phase with current.

Phase angle is the angle between the current vector and applied voltage vector.  This results in an RC Circuit where the applied voltage lags current somewhere between zero degrees and 90 degrees, depending on the relative amount of capacitive reactance and the resistance.  If the capacitive reactance is much greater than the resistance, then the phase angle is nearer 90 degrees, and if the resistance is much larger than the capacitive reactance, the phase angle is nearer 0 degrees.  If the applied voltage lags the current, the circuit is said to be capacitive regardless of the relative amount of capacitive reactance and resistance.

      

The figure on the right shows a resistor and capacitor connected in series across a voltage source.  The figure on the left depicts a vector diagram of the circuit on the right.  Ec, Ea and Er are called “vectors”.  A vector indicates both magnitude and direction.  The horizontal line is the  current vector, the vertical line represents the voltage across the capacitor.  The angle between the current vector and the applied voltage vector is called the phase angle and is always less than 90 degrees.

A reactance chart can be used to determine vector sum and phase angle.

 

Impedance

Impedance is not a vector quantity since it does not indicate phase, only amount. The value of Z can be determined using the Pythagorean Theorem to solve the unknown side of a right triangle. Z = the square root of (XL² + XC²).

Power of an RC circuit is determined the same as in a RL circuit. (P = E x  I cosθ).

 

Series RCL Circuits.

Any circuit containing a number of resistors, capacitors and coils connected in series can be simplified to a single value for resistance, capacitance and inductance.

Since capacitive reactance causes current to lead voltage and inductive reactance causes current to lag voltage, the two reactance’s are opposite in effect.  If XL is greater, the circuit will be considered inductive.  If XC is greater, the circuit will be considered capacitive.  Impedance (Z) can be found by using the right triangle method.

  

 

 

 

 

 

RCL circuit

In the series circuit , to find impedance (Z):
                  
      30Ω - 20Ω = 10Ω   Therefore XL = 10Ω
                   Z² = 10² + 10² = 200
                   Z = 14.14Ω

To find current (I): 

                   I = Ea / Z = 24 / 14.14 = 1.7 amps.

To find the voltage across the individual components:

                   Er = I x R = 1.7 x 10 = 17 volts
                   EL = I x XL = 1.7 x 30 = 51 volts
                   Ec = I x Xc = 1.7 x 20 = 34 volts

Note:  When the voltage across each component of this circuit is known, the applied voltage can be calculated:

                   Ea² = (51 – 34)² + 17² = 578
                   Ea = 24 volts

The above circuit is considered to be inductive becaus EL is greater than EC

 

Series LC Circuits

If a series circuit contains both inductive and capacitive reactance, the effective reactance is the difference between the two.  Resistance will be mostly due to the resistance in the coil.  When Xc and XL are equal, the only opposition to current is the resistance of the components themselves.  This type of circuit is called a series resonant circuit, a tuned circuit.

If a variable frequency source is applied to this circuit, there will be a particular frequency that will cause XL to equal Xc because both XL and Xc depend upon the frequency of the applied voltage. 

  

 

 

 

 

 

 

Series RCL Circuit

In the circuit, XL and Xc are equal values.  R represents the resistance in the circuit, mostly due to the coil winding.  At the resonant frequency of this circuit, the total impedance will be 100 ohms because the effects of XL and Xc cancel each other.

At the  resonate frequency, current in the circuit can be calculated as follows:

                   I = 100 / 100 = 1 amp
Then:
                   EL = I x XL = 800 x 1 = 800 volts
                   Ec = I x Xc = 800 x 1 = 800 volts
                   Er = I x R = 100 x 1 = 100 volts

Note that the voltage across the Inductor and Capacitor is much greater than the applied voltage at the resonant frequency of the circuit.

The formula for calculating resonant frequency of an LC circuit is as follows:

                   fr = 1 / 2 π times the square root of LC.

                   Or   0.159 / square root of LC.

Therefore, regardless of the values of L and C, there will always be some frequency where the circuit will resonate.  At the resonate frequency, power will be at maximum value and impedance of the circuit will be reduced to the amount of resistance in the circuit as capacitive and inductive reactance are both minimized at resonance. An increase of either L or C will cause a decrease in frequency and a decrease in either L or C will cause an increase in frequency.

 

 

 

 

 

 

 

Power response to increasing frequency

The voltage and current present in a tuned circuit will be dependent on the amount of resistance in the circuit, mostly determined by the ohmic values of L and C in response to the applied frequency. At resonance, the values of  XL and Xc are at minimum, therefore the resistance in the circuit will determine the selectivity of which the circuit is capable.  Selectivity is the ability to select a narrow band of frequencies and reject all others.

 

Q of a Tuned Circuit

The ratio of inductive reactance to resistance is called Quality of Merit of a coil, (Q) and is expressed as follows:

                   Q = XL / R

The Q of a circuit is practically the same as the Q of the coil and the resistance is usually the resistance of the coil.  The Q of the circuit will be reduced if additional resistance is added to the circuit.  It is desirable to have a resonate circuit with a high value of Q in order to obtain the maximum amount of gain.

Tuned filters are at the heart of radio frequency communication.  Some engineers spend their careers studying, and designing filters for various special uses in electronics.  The scientist Tesla developed a coil in the latter part of the 19th century that enabled the high voltage tuned circuit that Marconi used to build his pioneering ship to shore radio communication system.  Since Marconi’s time, radio pioneers of the 20th century have taken the state of the art to heights that enable you to communicate with just about anyone that you choose that has a “cell phone”.  The microwave oven that is now common in household kitchens transforms 120VAC into a microwave frequency used to resonate a tuned cavity at a frequency that can be used to heat food.  What will man think of next.