Math Applications Flashcards
An impedance triangle is a convenient way to illustrate impedance in a _____________ circuit.
Series AC
Given the angle, how do you find pf?
Cos theta (adjacent/hypotenuse)
Given a ratio of side lengths (eg. O/H) how do you find the angle in degrees?
Inverse trig. function (eg. Sin^-1)
What is the total opposition to the flow of current in an ac cct?
Impedance
What type of reactance causes current to lag voltage?
Inductive
What type of ractance causes current to lead voltage?
Capacitive
What is impedance?
- Total opposition to current flow in an AC CCT.
- The combination of resistance and total reactance (inductive and capacitive)
What circuit property opposes change in current by inducing electromagnetic force?
Inductance
What is a Henry and what does it measure?
A henry is when a current change of one ampere per second induces a voltage of one volt. It measures inductance.
What circuit property limits amount of current flow in an AC cct?
Inductive reactance and capacitive reactance
If a DC cct contains a coil with the property of inductance, how much inductive reactance will this cct have?
None. Inductive reactance requires a changing current.
How does inductive reactance change as frequency and inductance change in a cct?
It changes proportionally. Ie. Directly proportional.
Calculate the inductive reactance of a 0.3H coil when it is connected to a 60Hz supply
113 ohms
___________________ causes current to lag voltage by 90 degrees
Inductive reactance
What is capacitance?
- A circuit property
- allows a cct to store energy in electrostatic field and release is back into the cct.
What cct property opposes change in voltage?
Capacitance
What is a farad and what does it measure?
- when a change on 1V results in a charge of 1coulomb
- capacitance
____________________causes current to lead voltage by 90 degrees
Capacitive reactance
What is the capacitive reactance of a 30microfarad capacitor connected to a 50Hz supply?
106.1 ohms
Define “phase angle”
Number of degrees by which CURRENT through a component leads or lags the VOLTAGE across the component.
What trig. function is associated with pf?
Cosine
What are two methods of calculating voltage drop across a coil?
1) determine impedance (Z) and apply ohms law: Vcoil= Icoil x Zcoil
2) calculate phasor sum of Vdrops due to inductive reactive (opposite or y-axis or out-of-phase) and resistive (adjacent or x-axis or in-phase) components if the coil.
How would you find voltage drop across the capacitor?
V(Xc) = I(cap) x Xc
What other circuit property is Xc equal to?
Z(cap). Impedance if the capacitor
What is the in-phase power component?
Real, true, or active power (P) in watts
What is the out-of-phase power component?
Reactive power (Q) measured in vars
What is the additive result of active power and reactive power?
Apparent power (S) measured in VA
What formulas are used to find total apparent power (S(t)), total active power (P(t)), and total reactive power (Q(t)) of a circuit?
S(t) = I^2 x Z or S(t) = E x I(t) *this one is better*
P(t) = I^2 x R or P(t) = E x I(t) x pf (cos theta)
Q(t) = I^2 x X(t) Q(t) = E x I(t) x sin theta Q(t) = Q(Xl) - Q(Xc)
What trig. function is related to finding total apparent power in a circuit?
Sin
How does the relationship between sides of a triangle change from an impedance triangle to a power triangle of the same series circuit?
It does not. Relationships (pf) stay same
What is the reference for a series phasor diagram, and why?
Current because it’s common to every circuit component.
Where are the following volt drops drawn on a series phasor diagram:
1) Vr
2) V(XL)
3) V(XC)
4) V(coil)
1) in phase with current
2) leading current by 90° (positive y-axis)
3) lagging current by 90° (negative y-axis)
4) leading current by the phase angle of the coil
*but we use current as a reference to determine the terminology of leading or lagging, example: “current lags an inductive voltage drop” or “current leads an inductive voltage drop”
When can you use impedance diagrams for parallel RLC circuits?
When solving INDIVIDUAL BRANCHES
How do we find total current in a parallel RLC circuit?
1) phasor sum of all currents that flow through each branch
How do we find total impedance in a parallel circuit?
Ztotal = E / Itotal (ohms law)
What is the pf in parallel branch circuits with a resistor?
1; unity
What is the impedance equal to in a parallel branch with only a resistor?
Impedance is equal to resistance.
Z(r) = R(r); straight horizontal line, pf = 1
What is the pf in a parallel branch circuit with a capacitor?
0, 90° leading out-of-phase, straight vertical line
What is the impedance equal to in a parallel branch with only a capacitor?
Capacitive reactance, Z(cap) = Xc, pf=0
Once you have the total current of a parallel circuit, how do you find the overall pf?
Dividing in-phase component of current (x-axis) by the total current (phasorily added).
Ie. Adjacent/Hypotenuse = cos(theta) = pf
What is the relationship between capacitors reactive power and coil reactive power?
180° out of phase
How do you find total power of a parallel circuit?
Sum the power of the individual branches
What’s the power of a capacitor?
0W
How do you calculate the total reactive power of a parallel circuit?
Sum the reactive power of the individual branches
What is the reactive power of a resistor?
0var
How do you calculate total apparent power of a parallel circuit?
S= square root of (total power squared + total reactive power squared)
S= E x I(total)
S = current squared x total impedance
How do you find pf of a parallel circuit?
Pf = power/ apparent power or Pf= in-phase component of current/total current
What is the reference for a parallel phasor diagram?
Voltage
In a parallel phasor diagram, a phasor representing ___________ (leading or lagging) current is shown counter-clockwise from the reference voltage.
Leading
What should a phasor diagram include?
- Voltage reference
- Current through each branch
- phase angle of each branch
- total circuit current
- circuit phase angle
How many line voltages are there in a 3-phase wye-connected circuit?
- Vab, Vbc, Vca.
How many phase voltages are there in a 3-phase wye-connected circuit? Include subscript names.
- Van, Vbn, Vcn
What is the relationship between phase and line voltages in a balanced wye-connected load? (magnitude and angle)
Line V is 1.732 times larger
Line V leads phase V by 30°
What is the relationship between phase current and line current in a wye-connected load?
They are equal to eachother
How do you find the magnitude of the neutral current in a for a wye-connected circuit?
Phasor sum of the three line currents
What equations would you use to find the power components of a balanced three phase motor with a pf of 0.8lag?
S(motor) = sqr root of 3 x line voltage x line current
P(motor) = sqr root of 3 x line voltage x line current x 0.8
Q(motor) = sqr root of 3 x line voltage x line current x sin theta
Where are the following components drawn on a balanced wye-phasor diagram?
1) Van
2) Vbn
3) Vcn
4) Vab
5) Vbc
6) Vca
7) Icn
8) Ibn
9) Ian
1) Van = phase voltage @ 0°
2) Vbn = phase voltage @ 240°
3) Vcn = phase voltage @ 120°
4) Vab = line voltage @ 30°
5) Vbc = line voltage @ 270°
6) Vca = line voltage @ 150°
7) Icn = phase current in-phase with phase voltage @120°
8) Ibn = phase current @ 240°
9) Ian = phase current @ 0°
How would you find I(a) for an unbalanced delta connected load?
I(ab) + I(ac)
In a balanced three-phase delta-connected load, the line current is always ________ larger than its phase currents
1.732 times
Describe the following relationships in a balanced three-phase delta-connected load at unity power factor:
1) phase currents vs phase voltages
2) line current vs. Phase current
3) line current vs. Line voltage
4) line currents vs. Other line currents
5) phasor sum of line currents?
1) in phase with eachother
2) phasor located between the two relevant phase currents, value of line current is equal to phasor sum of the two relevant phase currents, and I(line) = I(phase) x square root of 3
3) line current lags their line voltage by 30°
4) displaced from eachother by 120°
5) 0
Where is I(ab)? No lag
0°
Where is I(ba)? No lag
180°
Where is I(bc)? No lag
240°
Where is I(cb)? No lag.
60° (240-180)
Where is I(ca)? No lag.
120°
Where is I(ac)? No lag
300° (120-180)
How do you determine the phase values of power in a balanced three-phase circuit, given the total power components?
Devide total power component by 3
How do you find the total power components of a balanced multi-load three-phase system?
P(total) = sum of total power from each component
Q(total) = sum of reactive power from each component
S(total) = pythagorean theorem using vertical and horizontal components (true and reactive power components)
Compare the power dissipated by a delta-connected load vs. that same load connected in wye.
Power dissipated in delta is 3 times larger
How can wye and dela supply the same apparent power (if each is connected to the same source)?
Wye supplies higher voltage at lower current, while delta supplies higher current at lower voltage.
What is the line current of an alternator with a maximum of 100A per phase connected in:
A)delta
B)wye
A)173A
B)100A
What happens to the output line voltage when a three-phase alternator is reconnected from a wye to a delta?
It is reduced by 1.73
