AC theory and calculations Flashcards
What is AC frequency:
A measure of the number of cycles per second
Unit hertz
1/time period
What is the the units for angular frequency
The symbol
the formula that relates is to frequency measured in hertz
2(π)frequency (hz)
Units is radians per second
Symbol omega (ω)
What is the amplitude of a ac sine wave
The maximum voltage measured from zero to maximum (not from max positive to max negative).
What is the period in an ac sin wave
The time period for one full cycle. E.g from max positive to max positive. Not from max positive to max negative.
What is the formula for voltage as a function of time in an ac sine wave
V(t)= (Vm) sin(omega x time + theta)
Vm: is voltage maximum within a given sine wave. Unit: volts
Omega w: is angular frequency. This is related to the regular frequency measured in hertz by the formula 2(pi)frequency. Unit: radians per second.
Theta: is the phase angle. Unit degrees or more typical radians. This tells where the sine wave begins on the Y intercept. Therefore is shifts the wave left or right.
What is phase angle on a AC sine wave.
Phase angle dictates where the AC sign wave or cosine wave starts on the Y intercept. It does not change the shape or amplitude of the wave but it shifts it left an right relative to time. The symbol is theta. A positive theta value indicates that a sine wave starts on the downwards slope of the wave. A negative value indicates it starts on the upward slope of the wave.
What is RMS voltage
Root mean squared voltage is an average of an AC voltage that gives it an approximate DC equivalent.
The formula is Voltage max/ √2.
Describe polar coordinates of complex numbers:
Complex numbers can be represented as a co-ordinate pair on a grid with the real part of the complex number on the x axis and the imaginary part on the y axis.
The polar representation of a complex number is when you transform it into a vector.
The real part of the number forms the adjacent (horizontal) side. The complex part of the number forms the opposite (vertical) side. Using pythagorus you can work out the length of the hypotenuse. Using sohcahtoa you can work out the angle from the origin.
This is represented in polar notation as: magnitude(e^i(angle))
For example if the length is 3 and the angle is 45 degrees.
3(e^45i)
Using pythagorus theorem you can.
What is Eulers identity
e^i(theta) = cos(theta) + (j)sine(theta)
This can be expressed as:
Cos(theta) = (the real part only) of: e^j(theta) Sin(theta) = (the imaginary part only) of: e^j(theta)
This can be applied the formula to find instantaneous Voltage in an AC sine wave. V(t) = (Vmax) Cos (omega x T + theta)
Voltage as a function of time = (max voltage) cos (angular frequency x time + phase angle)
V(t) = (the real part only of): = V(m) x e^j(theta) x e^j(omega)t
Express the following instantaneous voltage equation in phasor notation
V = 170 cos (337t - 40(degrees))
V = 170 (angle symbol) 40⁰
The frequency components (omega x time period) are left out of the circuit calculations and added back only with the final answer because they always remain constant within a given circuit and it makes calculations simpler to omit them.
What is the process for adding phasors
A phasor is and angle and magnitude. It can be thought of as the hypothenuse of a right and triangle. The vertical side of the triangle is the imaginary component and the horizontal side is the real component. Convert the two phasors into algebraic form complex numbers (real part + imaginary part). Add the two complex numbers and convert the result back into phasor form using trigonometry.
How do resistors capacitors and inductors affect the power factor.
Resistors do not affect power factor
Inductors cause current to lead voltage
Capacitors cause current to lag voltage
What is instantaneous voltage in an inductive AC circuit
V = L x di/dt
Voltage equals the inductance multiplied by the derivative of the current with respect to time.
Inductance unit henry (H)
This causes the voltage to lead the current in an inductive circuit.
