Module 3.14 — Resistive, Capacitive and Inductive AC Circuits
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573 Terms
What three passive circuit components are studied in BA 3.14?
Resistors, inductors and capacitors.
What do R, L and C represent?
Resistance, inductance and capacitance.
What does RLC stand for?
Resistance, Inductance and Capacitance.
What is the main difference between DC and AC circuit behaviour?
AC quantities change with time and reactive components can cause phase differences.
What is phase difference?
The angular separation between corresponding points on alternating waveforms.
What symbol is used for phase angle in BA 3.14?
θ (theta) or φ (phi).
What units are used for phase angle?
Degrees or radians.
What is meant by two waveforms being in phase?
They reach their corresponding maximum, minimum and zero values at the same time.
What is meant by current leading voltage?
Current reaches corresponding waveform points earlier than voltage.
What is meant by current lagging voltage?
Current reaches corresponding waveform points later than voltage.
What is a phasor diagram?
A vector diagram representing the magnitude and phase of sinusoidal electrical quantities.
Why are phasor diagrams useful for AC circuits?
They allow out-of-phase voltages or currents to be combined correctly.
Can out-of-phase AC magnitudes always be added using ordinary arithmetic?
No; they must be combined as phasors.
What is a purely resistive AC circuit?
An AC circuit containing resistance without inductive or capacitive reactance.
What is the relationship between voltage and current in a pure resistor?
They are in phase.
What is the phase angle in a purely resistive AC circuit?
0°.
When does current reach its positive maximum in a pure resistive circuit?
At the same time as voltage reaches its positive maximum.
When does current cross zero in a pure resistor?
At the same time as voltage crosses zero.
What happens to resistor current as applied AC voltage increases?
It increases proportionally.
What happens to resistor current as applied AC voltage decreases?
It decreases proportionally.
What is the current formula for a purely resistive AC circuit?
I = V/R.
What is the impedance of a pure resistor?
Z = R.
What does Z represent in an AC circuit?
Impedance.
What is impedance?
The total opposition to alternating current.
What is the unit of impedance?
Ohm (Ω).
What is the impedance formula using RMS voltage and current?
Z = V/I.
What is the phase relationship shown in BA Figure 2?
Resistor current and voltage are in phase.
What does BA Figure 3 illustrate?
Coincident voltage and current phasors for a pure resistor.
What is the mnemonic CIVIL used for?
Remembering current and voltage phase relationships in capacitors and inductors.
What does CIV mean in CIVIL?
In a Capacitor, Current (I) leads Voltage (V).
What does VIL mean in CIVIL?
In an Inductor (L), Voltage (V) leads Current (I).
What is the phase difference in an ideal pure capacitor?
Current leads voltage by 90°.
What is the phase difference in an ideal pure inductor?
Current lags voltage by 90°.
What is the phase difference in an ideal pure resistor?
0°.
Which component has current leading voltage?
A capacitor.
Which component has current lagging voltage?
An inductor.
Which component has voltage and current in phase?
A resistor.
Why is the phase difference in a real RL or RC circuit generally less than 90°?
Resistance contributes an in-phase component.
What does an inductor store energy in?
A magnetic field.
What happens when current through an inductor changes?
A self-induced EMF is produced.
What does an inductor's self-induced EMF oppose?
The change in current.
What law explains the direction of self-induced EMF?
Lenz's Law.
What happens to an ideal inductor after its DC current becomes constant?
Its self-induced EMF falls to zero.
What is the approximate time for DC current to become practically steady in an RL circuit?
Five time constants.
What is the RL time constant formula?
T = L/R.
What is the approximate RL current growth time used in BA 3.14?
5L/R.
Why does an inductor behave differently on AC and steady DC?
AC continually changes current and produces self-induced EMF.
What is inductive reactance?
Opposition to alternating current caused by inductance.
What symbol represents inductive reactance?
XL.
What is the unit of inductive reactance?
Ohm (Ω).
What is the formula for inductive reactance?
XL = 2πfL.
What does f represent in XL = 2πfL?
Frequency in hertz.
What does L represent in XL = 2πfL?
Inductance in henries.
What does π represent in XL = 2πfL?
The mathematical constant pi.
What approximate value of π is normally used in calculations?
3.14.
How does inductive reactance change when frequency increases?
It increases.
How does inductive reactance change when frequency decreases?
It decreases.
How does inductive reactance change when inductance increases?
It increases.
How does inductive reactance change when inductance decreases?
It decreases.
What happens to XL if frequency doubles at constant inductance?
It doubles.
What happens to XL if frequency halves at constant inductance?
It halves.
What happens to XL if inductance doubles at constant frequency?
It doubles.
What happens to XL if inductance halves at constant frequency?
It halves.
What happens to XL if both frequency and inductance double?
It becomes four times as large.
What happens to XL if frequency doubles and inductance halves?
It remains unchanged.
What relationship exists between inductive reactance and frequency?
Direct proportionality.
What relationship exists between inductive reactance and inductance?
Direct proportionality.
What happens to ideal inductive reactance as frequency approaches zero?
It approaches zero.
How does an ideal inductor behave towards steady DC after transients disappear?
Like a short circuit.
What happens to ideal inductive reactance as frequency becomes extremely high?
It becomes very large.
How does an ideal inductor behave at very high frequency?
It strongly opposes current.
At fixed RMS voltage, what happens to current through a pure inductor when frequency increases?
Current decreases.
At fixed RMS voltage, what happens to current through a pure inductor when frequency decreases?
Current increases.
What formula gives current through an ideal pure inductor?
I = V/XL.
What happens to pure-inductor current if XL doubles at constant voltage?
It halves.
What happens to pure-inductor current if XL halves at constant voltage?
It doubles.
What is the phase relationship of voltage and current in a pure inductor?
Voltage leads current by 90°.
What is the equivalent statement about current in a pure inductor?
Current lags voltage by 90°.
How much of a complete cycle is 90°?
One-quarter.
How much later does pure-inductor current reach its maximum compared with voltage?
One-quarter cycle.
Does the 90° ideal inductive phase angle change merely because frequency increases?
No; for an ideal pure inductor it remains 90°.
What happens to ideal-inductor current magnitude when frequency increases at unchanged voltage?
It decreases.
What happens to inductive back EMF as the rate of current change increases?
Its magnitude increases.
What does BA Figure 5 illustrate?
Voltage leading current by 90° in an ideal inductive circuit.
What does BA Figure 6 illustrate?
Phasors showing current lagging voltage by 90°.
What does BA Figure 7 illustrate?
Inductive reactance increasing with frequency.
What does BA Figure 8 illustrate?
Inductive reactance approaching zero as frequency approaches DC.
What is the mathematical relationship between XL and f for fixed L?
A straight-line increase.
What is an RL circuit?
A circuit containing resistance and inductance.
What does series RL mean?
A resistor and inductor connected in a common current path.
What is the current relationship in a series RL circuit?
The same current flows through both components.
Why does a real coil usually have resistance?
Its winding wire has electrical resistivity.
How can a real inductive coil be represented electrically?
As resistance in series with inductance.
Why is a real inductive circuit's phase angle normally less than 90°?
Winding resistance creates an in-phase voltage component.
What quantity is used as the reference when drawing a series RL phasor diagram?
Current.
Why is current the reference in a series RL phasor diagram?
It is common to all series components.
What is the phase relationship between VR and series current?
VR is in phase with current.
What is the phase relationship between VL and series current?
VL leads current by 90°.
What is the resistor voltage formula in a series RL circuit?
VR = IR.
What is the inductor voltage magnitude formula in a series RL circuit?
VL = IXL.