2-6) AC-RCL Circuits

Question 1

What does RCL stand for?

Answer 1

Resistor, Capacitor, Inductor

Question 2

What is the relationship between inductance and capacitance?

Answer 2

They oppose each other.

Question 3

Explain what this diagram represents.

Answer 3

Z_T represents total impedance–the resistance to AC in a reactive circuit. Inductance (X_L) and capacitance (X_C) opposite each other, so their arrows point in opposite directions. Resistance (R) is 90 degrees out of phase to both X_L and X_C, so it’s arrow points to the right, 90 degrees from X_L and X_C. In a resonant circuit where X_L and X_C are equal and cancel each other out, the circuit resembles a purely resistive circuit.

Question 4

For a fixed resistor, explain these values:

R = 100Ω

X = 0Ω

Z = 100Ω ∠0°

Answer 4

R = 100Ω fixed resistance

X = 0Ω reactance, because a resistor is not a reactive component. Its resistive value does not change in an AC circuit compared to a DC circuit

Z = 100Ω ∠0° because the resistance is fixed. The phase angle is 0° because applied current and applied voltage are 0° out of phase (they are in phase) in a purely resistive circuit

Question 5

For an inductor, explain these values:

100mH

159.15Hz

R = 0Ω

X = 100Ω

Z = 100Ω ∠90°

Answer 5

100mH: the value of the inductor is expressed in the unit “Henry.” This inductor is 100mH (milli Henry)

159.15Hz: AC frequency will determine inductive reactance. Given a frequency of 159.15Hz, the inductive reactance is 100Ω

R = 0Ω is the resistance of the inductor because it only resists AC current. In a DC circuit, an inductor will just act as a coil of wire–a conductor

X = 100Ω is the resulting inductive reactance of this 100mH inductor in a 159.15Hz AC circuit (X_L=2∏fL = 2 x 3.14 x 159.15Hz x 0.1H = 100Ω)

Z = 100Ω ∠90° because 100Ω is the resulting impedance in this reactive circuit. ∠90° is the phase angle because Voltage Leads Current (ELI) in an inductive circuit. The phase angle will change as frequency changes.

Question 6

How does an inductor work?

Answer 6

An inductor is an electronic component that is used to produce inductance in a circuit. A coil connected to a source of DC builds up a magnetic field when the circuit is closed. The expanding magnetic field cutting across the coil windings induces a counter electromotive force (CEMF). This voltage opposes the source voltage and opposes the rise in current. When the current reaches maximum value, there is no further change in the current. Consequently there is no longer an induced CEMF. The current is now only limited by the ohmic resistance of the wire. If the voltage source is disconnected, current in the circuit falls to zero. As the current falls to zero, the magnetic field collapses. As the magnetic field collapses, it again induces CEMF. This CEMF is in the opposite direction of the CEMF created when the coil was energized. This CEMF now slows the reduction in current by feeding current back into the circuit as the magnetic field collapses. Inductors resist changes in current.

Question 7

What are four factors that dictate an inductor’s inductance? Explain each factor.

Answer 7

1. Number of coils–more coils means more inductance
2. Material that the coils are wrapped around (the core)
3. Cross-sectional area of the coil–more area means more inductance
4. Length of the coil-a short coil means narrower (or overlapping coils), which means more inductance

Question 8

What is the formula to calculate the inductance (in Henries) in an inductor?

Answer 8

L=4π10^-7 x (N² X A) / ℓ

L=Henries

μ_ο=Permeability of Free Space (4π10^-7)

N=Number of turns

A=Inner Core Area (πr ²) in m²

ℓ=length of coil in meters

Question 9

How is a capacitor constructed?

Answer 9

Terminals connect to two metal plates that are separated by a non-conducting substance called a dielectric.

Question 10

What types of substances are typically used as dielectrics?

Answer 10

Mica, ceramic, cellulose, porcelain, mylar, teflon or air.

Question 11

What factors will determine the proper application for a capacitor?

Answer 11

Size and type of dielectric

Question 12

For a capacitor, explain these values:

10 μF

159.15Hz

R = 0Ω

X = 100Ω

Z = 100Ω ∠-90°

Answer 12

10μF: the value capacitance for the capacitor is expressed in the unit “Farad.” This capacitor has 10μF (microFarad) capacitance

159.15Hz: AC frequency will determine capacitive reactance. Given a frequency of 159.15Hz, the capacitive reactance is 100Ω

R = 0Ω ??? Not infinite in DC?

X = 100Ω is the resulting capacitive reactance of this 10μF capacitor in a 159.15Hz AC circuit (X_C=1/2∏fL = 1 / (2 x 3.14 x 159.15Hz x 0.00001F = 100Ω)

Z = 100Ω ∠90° because 100Ω is the resulting impedance in this reactive circuit. ∠-90° is the phase angle because Current Lags Voltage (ICE) in a capacitive circuit. The phase angle will change as frequency changes.

Question 13

How might an air capacitor be used?

Answer 13

Often used in radio tuning circuits.

Question 14

How might a mylar capacitor be used?

Answer 14

Most commonly used for timer circuits like clocks, alarms and counters.

Question 15

How might a glass capacitor be used?

Answer 15

Good for high voltage applications

Question 16

How might a ceramic capacitor be used?

Answer 16

Used for high-frequency purposes like antennas, X-ray and MRI machines

Question 17

How much a super-capacitor be used?

Answer 17

Power electric and hybrid cars

Question 18

What is capacitance?

Answer 18

Capacitance is the property that opposes any change in voltage.

Question 19

What is a capacitor and how does it work?

Answer 19

A capacitor is a device that temporarily stores en electric charge. A capacitor accepts or returns this charge in order to maintain constant voltage.

Question 20

What is the unit of capacitance?

Answer 20

Capacitance is a capacitor’s storage potential and is measured in units called Farads. A 1-Farad capacitor can store 1 coloumb of charge at 1 volt. Because 1 amp represents an electron flow rate of 1 coloumb of electrons per section, a 1-Farad capacitor can hold 1 amp-second of electrons at 1 volt.

Question 21

What size are capacitors typically measured in?

Answer 21

Capacitors are typically measured in micro or pico Farads.

Question 22

What is reactance? What are its symbols and what are its units?

Answer 22

Reactance is electrical impedance, a measurement of opposition to a sinusoidal alternating current. Capacitive Reactance is X_C, Inductive Reactance is X_L. Its units are measured in ohms.

Question 23

What causes reactance?

Answer 23

Reactance arises from the presence of inductance and/or capacitance within a circuit created in inductors and capacitors.

Question 24

How are reactance, resistance and impedance related?

Answer 24

Impedance is the total resistance in a circuit that takes resistance, inductive reactance and capacitive reactance into the total measurement.

Question 25

What is inductive reactance (X_L)

Answer 25

X_L is associated with the expanding and contracting magnetic field that surrounds a wire or coil carrying a current. The more rapidly the current changes, the more an inductor resists it.

Question 26

What is the relationship between frequency and inductive reactance?

Answer 26

Inductive reactance is proportional to frequency. High frequency AC changes more rapidly than low-frequency AC. Higher frequency increases inductive reactance and current flow meets more opposition.

Question 27

What is capacitive reactance (X_C)?

Answer 27

XC is associated with changing electric field between two conductive surfaces (plates) separated from each other by an insulating dielectric medium in a capacitor. The more rapidly the applied voltage changes in value, the faster the capacitor stores energy. This means that a high-frequency AC will put more current into a capacitor than low frequency. Capacitive reactance decreases as frequency increases.

Question 28

Explain this diagram. What does it mean if X is greater, equal or less than 0?

Answer 28

Reactance produces a phase shift between current and voltage in a circuit. Reactance is denoted by the symbol X and is measured in ohms.

If X > 0, reactance is said to be inductive

If X = 0, then the circuit is purely resistive (i.e. it has no reactance)

If X < 0, it is said to be capacitive

Question 29

What is the relationship between Inductive Reactance (X_L), frequency (f) and inductance (L)?

Answer 29

X_L is directly proportional to frequency and inductance.

If frequency increases, then X_L increases proportionally.

If inductance increases, then X_L increases proportionally.

Question 30

What is the formula to computer total inductive reactance in a series circuit?

Answer 30

X_LT = X_L1 + X_L2 + X_L3 +…….X_LN

Question 31

Explain the concept of mutual inductance and what affects the degree/amount of mutual inductance.

Answer 31

Whenever two coils are located so that the flux from one coil links with the turns of the other coil, a change of flux in one coil causes an EMF to be induced in the other coil. This allows the energy from one coil to be transferred or “coupled” to the other coil. The two coils are said to be coupled or linked by the property of mutual inductance (M). Any current drawn through the secondary coil to power a load induces a corresponding current in the primary coil, drawing current from the source. The primary coil is behaving like a load on the AC source. The secondary coil behaves like a source on the resistor.

The amount of mutual inductance depends on the relative positions of the two coils. If the two coils are separated by a considerable distance, the amount of flux common to both coils is small and the mutual inductance is low. Conversely, if the coils are close together so that nearly all the flux of one coil links to the turns of the other, mutual inductance is high. Mutual inductance can be increased greatly by mounting the coils on a common iron core.

Question 32

How do you calculate total inductive reactance in a series circuit?

Answer 32

Just add up the total of inductive reactance for each inductor. To make it easier, you can add up the total inductance for all inductors in series and calculate inductive reactance once.

X_LT=X_L1+X_L2….

Question 33

What is the relationship between capacitive reactance, capacitance and frequency?

Answer 33

Capacitive reactance (X_C) is inversely proportional to both frequency and capacitance.

If frequency increases, then X_C will decrease.

If capacitance increases, then X_C will decrease.

Question 34

How do you calculate total capacitive reactance in a series circuit?

Answer 34

Add the values together:

X_CT=X_C1+X_C2+X_C3+…..X_CN

Question 35

What are 3 different formulas to calculate total capacitance (C_T) of series capacitors? How are each used?

Answer 35

2 capacitors of different value: C_T = C₁ x C₂ / C₁ + C₂

3 or more capacitors of different value: C_T = 1 / (1/C₁ + 1/C₂ + 1/C₃)

2 capacitors of the same value: C_T = C(½)

Question 36

How do you calculate total Capacitive Reactance in a Parallel Circuit?

Answer 36

XCT = 1 / (1/X_C1 + 1/X_C2 + 1/X_C3)

Question 37

What term refers to the resistance produced by capacitors and inductors?

Answer 37

Impedance

Question 38

What is the phase relationship between voltage and current in a purely resistive circuit?

Answer 38

In Phase

Question 39

How are RCL Vectors used?

Answer 39

RCL Vectors help us visualize the relationship between voltage, current and impedance on a graph. These vectors can be plotted as either positive or negative with reference to the horizontal 0 line pointing to the right.

Question 40

Why does the plot range between 180° and -180°

Answer 40

The maximum out of phase any two components can be is 180 degrees. If the vector value is 0° (horizontal right), then the vector is considered to be in phase. Anything greater than or less than 0° is out of phase.

Question 41

What does each of the variables represent in this graph?

Answer 41

This is an RCL vector plot showing:

I_T = total current

R = resistor value

I_L, I_C and I_R = current through each component. They are equal because in a series RCL circuit the same current is going through all components.

E_R = applied voltage that is the same for all of the components in the series circuit.

Z = Impedance

Question 42

Explain how to interpret this graph.

Answer 42

E_R is voltage across the resistor.

I is current, which is in phase with voltage across the resistor.

E_C and E_L are both 90° out of phase with current.

Voltage across the inductor E_L is leading current by 90° (ELI).

Voltage across the capacitor E_C is lagging current by 90° (ICE).

Question 43

What is impedance and what determines if it’s positive or negative?

Answer 43

Impedance (Z) is the total opposition of a circuit to alternating current. Capacitive Reactance or Inductive Reactance determines if the value is positive or negative.

Question 44

Describe the steps required to calculate total impedance and total current in this series RCL circuit.

Answer 44

1. Calculate (X_L) for the 27mH inductor using the formula: X_L = 2∏fC
2. Calculate (X_C) for the 380μF capacitor using the formula: X_C = 1/2∏fC
3. Calculate total impedance using the formula: Z_T=(√R²+(X_L-X_C)²)
4. Calculate total current using the formula: I_T=V_A/Z_T

Question 45

How does applied voltage distribute in a parallel RCL circuit?

Answer 45

The same as in a parallel DC circuit. All branches have the same applied voltage in common. Voltage is common in a parallel circuit.

E_a=E_R=E_L=E_C

Question 46

How does current distribute in a parallel RCL circuit? How is current tabulation different in a parallel RCL circuit compared to a series RCL circuit?

Answer 46

Resistor current is in phase with applied voltage. Capacitor current leads applied voltage (ICE) by 90°. Inductor current lags applied voltage (ELI) by 90°. Current calculation is different in a parallel circuit because individual branch currents must be added separately according to their respective reactance values. Branch currents are added together to get the total current.

Question 47

What are the steps you would take to solve for impedance and total current in this parallel RCL circuit?

Resistor = 4Ω

Inductor = 27mH

Capacitor = 380μF

Applied Voltage = 110V

Frequency = 60Hz

Answer 47

1. Calculate X_L using the formula X_L = 2∏fC
2. Calculate X_C using the formula X_C = 1/2∏fC
3. Calculate X_T using the formula X_T = X_L x X_L / X_L - X_C
4. Calculate ZT using the formula ZT = R x XT /

Question 48

What is a resonant circuit condition?

Answer 48

A condition where the capacitive and inductive reactance of an LC circuit are equal. Capacitors store energy in the form of an electric field and electrically manifest that stored field as a potential: static voltage. Inductors store energy in the form of a magnetic field and electrically manifest that stored energy as a kinetic motion of electrons: current. Capacitors and Inductors mirror each other, storing and releasing energy in complementary modes.

Question 49

What is displayed in this graph?

Answer 49

When an inductor and capacitor are connected in series, the two components will exchange energy between them, back and forth. If a momentary voltage is applied to both components at a specific frequency, the capacitor will charge very quickly and the inductor will oppose a change in current, leaving the capacitor charged and the inductor discharged.

When current is at maximum, the impedance is at minimum when operating at the resonant frequency. This is only true for series RCL circuits.

In a parallel RCL circuit, the plot will show the opposite–when operating at resonance, when total impedance is at maximum, total current is at a minimum.

Question 50

Explain what this diagram shows as it relates to bandwidth and bandpass.

Answer 50

At the resonant frequency (f_R) in the center (1.5kHz), impedance is at minimum and current is at maximum. On either side of f_R, there are 2 other frequencies called the Current Half-Power Points (I_HPP)–both above and below the f_R. At each of these I_HPP, current will equal 70.7% of maximum current that occurs at the f_R.

Bandwidth is the difference between the two half-power points f₁ and f₂. Bandpass If f₁ is 1kHz and f₂ is 2kHz, then the bandwidth for this circuit is 1kHz wide.

Bandpass is expressed as a range of I_HPP between high and low. In this example, bandpass is from 1kHz to 2kHz.

Question 51

Explain what this diagram shows as it relates to Circuit Impedance Half-Power Points

Answer 51

Overall circuit impedance (Z) can be plotted on a graph of frequency. Impedance half-power points (Z_HPP) are the two points on the impedance curve that are 70.7% of the peak impedance value. With these values, you can determine the bandpass and bandwidth.

This plot is normally used to describe parallel resonance circuit operation. This is because a parallel circuit is at resonance when the impedance is at maximum and current is at minimum.

Question 52

What is “Q” in circuit?

Answer 52

Q in a circuit is a description of quality of the circuit. This is because the various curves do pass the current half power point (I_HPP) at the same rate or stay above the I_HPP at the same levels. Q in a circuit can be caused by many things. It can be how fast components charge and discharge or how much resistance is in a circuit. Circuits are rated at either High Q or Low Q.

Q is the ratio of bandwidth to the peak current curve. The Q and the bandwidth are inversely proportional to each other. This means that a circuit with high Q will have a narrow bandwidth and a low Q circuit will have a wide bandwidth.

Question 53

How do you determine Q in a circuit and what’s the formula for Q?

Answer 53

Take the inductive reactance and divide by resistance. To control Q, you can change the circuit resistance.

Q = X_L / R

Question 54

What are the characteristics of a resonant circuit?

Answer 54

At a specified frequency, the voltage of the capacitor and the inductor are equal.

E_C = E_L

Inductive reactance and capacitive reactance equal each other, they cancel each other out and the circuit impedance is reduced to the value of the resistor(s).

Question 55

What is the difference between a Series and Parallel RCL Circuit?

Question 56

What is a tank circuit, what components is it made of and how does it work?

Answer 56

A tank circuit is the heart of an oscillator circuit made of one inductor and one capacitor wired in parallel. The only theoretical resistance is contained in these two components, although any real circuit has some resistance which causes dampening to occur with each oscillation and the amplitude is gradually reduced.

The amplifier supplies the initial energy to the capacitor, which charges. When it discharges, it energizes the inductor, creating a temporary magnetic field. As the field collapses, polarity is reversed and charges the capacitor again.

The output frequency of the oscillator is primarily the resonant frequency of the tank circuit components itself.

Question 57

What is the formula to determine the resonant frequency of a LC Network (Tank Circuit)?

Answer 57

F_r = 1 / 2 ∏√LC

Question 58

What is the flywheel effect principle?

Answer 58

The maintenance of oscillations in a circuit in intervals between pulses of excitation energy. The LC network provides initial oscillations. A portion of the output of the LC network is then returned to the input of the amplifier through the regenerative feedback network to sustain the oscillations.

When a tank circuit is used to develop oscillations in an oscillator, the output frequency of the oscillator is primarily the resonant frequency of the tank circuit.