Steady State AC Circuits Flashcards
Why use ac over dc
easier to generate and easier to change from one voltage to another
voltage at any time =
v(t) = Vp * sin(angular frequency * time)
What is Vp
Peak voltage
Symbol for angular frequency
omega
How to calculate angular frequency
2Pifrequency
frequency units
Hz
Relationship between frequency and time period
f=1/T
How to calculate root mean square voltage
Vrms = Vp / sqrt(2)
Mains supply in the UK
50Hz 230Vrms 325Vp
How to calculate current at any time in a circuit
i(t) = Ip*sin(angular frequency *t)
What is the reactance of a capacitor
1/ j2PifC, the j here is not necessary when calculating magnitude will have units of ohms
What is the phase difference between the current and the voltage waveform across a capacitor
the voltage lagging the current by 90 degrees, or the current leads the voltage by 90 degrees
What is the phase difference between the current and the voltage waveform across a resistor
Nothing they are in phase with each other, however the magnitude will be scaled by the magnitude of the resistance
What is the inductive reactance
2PifLj, j is there as a directional thing does not give the magnitude of the reactance
What is the phase difference between the current and the voltage waveform across a inductor
The current lags the voltage by 90 degrees or the voltage leads the current by 90 degress
What is the acronym to work out the phase difference
CIVIL, In a capacitor the current leads the voltage
in an inductor the voltage leads the current
When drawing phasor diagrams what is the usual position
choose the zero degree point for one of the phasors one along x axis
How do we normally express a phasor in elecrical engineering
Z
What is the symbol for capacative reactance
Xc in ohms
What is the symbol for inductive reactance
XL in ohms
What is the symbol of Impedance
Z
What is the update form of ohms law
v=iZ
When looking at series circuits what do you normally draw everything relative to
the current as it is constant for all
What will the angle between the capactior voltage and current always be
the voltage across the capactior will always be behind by 90 degrees or pi/2
What will the angle between the inductor voltage and current always be
the voltage across the inductor will always be ahead by 90 degrees or pi/2
Why does the resultant voltage and current not stay at constant phase difference for different circuits
as the values of the inductors and capacitors will change therefore their voltages will change, making the phase angle between the two of them vary
What are you generally looking for in ac circuit questions
will often be asked for the phase angle between the total voltage and current
in a inductor and resistor circuit whats the relationship to the supply voltage
vs = sqrt( vr^2 + vL^2) = square root of the resistors voltage squared plus the inductors voltage squared
at low frequencies what happens in an inductor plus resistor circuit and at high freq
low freq => omega => zero and magnitude of the impedance => R therefore phase angle between voltage and current => 0
high freq => omega => infinity and magnitude of the impedance => omega*L therefore phase angle between voltage and current => 90
at low frequencies what happens in an capacitor plus resistor circuit and at high freq
low freq => omega => zero and magnitude of the impedance => 1/omega*C => infinity therefore phase angle between voltage and current => -90
high freq => omega => infinity and magnitude of the impedance => R therefore phase angle between voltage and current => 0
difference between resistance and impedance
impedance has both phase and magnitude where as resistance only has magnitude
What is impedance
the measure of the opposition that a circuit presents to a current when a voltage is applied
What are the real parts and imaginary parts of impedance called
real is resistance and the imaginary part is reactance
What does the reactance part of impedance do
it causes a phase shift between the voltage and current, it is created due the capacitance or inductance
What do you normally calculate everything relative to in a parallel circuit
The voltage as it is constant for all
What is the resonant frequency
it is the frequency at which the circuit appears purely restive as the capacitor and inductor cancel each other out
what are components required in a resonant circuit
inductor, capacitor, resistor
what happens at resonance property wise for series
magnitude of vL=vC v=vr impedance = R phase difference = 0 and impedance will be at a minimum therefore current will be at a maximum
What is the Q factor
it is the magnification factor at resonance in series it is the voltage in parallel it is the current
How do you calculate the Q factor in series
magnitude of the inductor voltage (or capacitor voltage)/ the resistor voltage
(1/R)*sqrt(L/C)
What is the equation of resonance for a series and parallel circuit
1/(2Pisqrt(L*C))
difference between resonance for a parallel and a series circuit
in series the voltages are 180 degrees out of phase and of equal in magnitude
and in parallel the current is 180 degrees out of phase and equal magnitude
what happens at resonance property wise for parallel
magnitude of iL=iC i=ir impedance = R phase difference = 0 and impedance will be at a maximum therefore current will be at a minimum
What is the issue with having all three components in parallel and what is the solution
draw very large currents therefore the resistor is normally put in series
How do you calculate the Q factor in parallel
magnitude of the inductor current (or capacitor current)/ the resistor current
R*sqrt(L/C)
