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4th Year Electrical > Math Applications > Flashcards

Math Applications Flashcards

1
Q

An impedance triangle is a convenient way to illustrate impedance in a _____________ circuit.

A

Series AC

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2
Q

Given the angle, how do you find pf?

A

Cos theta (adjacent/hypotenuse)

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3
Q

Given a ratio of side lengths (eg. O/H) how do you find the angle in degrees?

A

Inverse trig. function (eg. Sin^-1)

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4
Q

What is the total opposition to the flow of current in an ac cct?

A

Impedance

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5
Q

What type of reactance causes current to lag voltage?

A

Inductive

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6
Q

What type of ractance causes current to lead voltage?

A

Capacitive

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7
Q

What is impedance?

A
  • Total opposition to current flow in an AC CCT.

- The combination of resistance and total reactance (inductive and capacitive)

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8
Q

What circuit property opposes change in current by inducing electromagnetic force?

A

Inductance

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9
Q

What is a Henry and what does it measure?

A

A henry is when a current change of one ampere per second induces a voltage of one volt. It measures inductance.

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10
Q

What circuit property limits amount of current flow in an AC cct?

A

Inductive reactance and capacitive reactance

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11
Q

If a DC cct contains a coil with the property of inductance, how much inductive reactance will this cct have?

A

None. Inductive reactance requires a changing current.

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12
Q

How does inductive reactance change as frequency and inductance change in a cct?

A

It changes proportionally. Ie. Directly proportional.

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13
Q

Calculate the inductive reactance of a 0.3H coil when it is connected to a 60Hz supply

A

113 ohms

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14
Q

___________________ causes current to lag voltage by 90 degrees

A

Inductive reactance

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15
Q

What is capacitance?

A
  • A circuit property

- allows a cct to store energy in electrostatic field and release is back into the cct.

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16
Q

What cct property opposes change in voltage?

A

Capacitance

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17
Q

What is a farad and what does it measure?

A
  • when a change on 1V results in a charge of 1coulomb

- capacitance

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18
Q

____________________causes current to lead voltage by 90 degrees

A

Capacitive reactance

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19
Q

What is the capacitive reactance of a 30microfarad capacitor connected to a 50Hz supply?

A

106.1 ohms

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20
Q

Define “phase angle”

A

Number of degrees by which CURRENT through a component leads or lags the VOLTAGE across the component.

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21
Q

What trig. function is associated with pf?

A

Cosine

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22
Q

What are two methods of calculating voltage drop across a coil?

A

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.

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23
Q

How would you find voltage drop across the capacitor?

A

V(Xc) = I(cap) x Xc

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24
Q

What other circuit property is Xc equal to?

A

Z(cap). Impedance if the capacitor

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25
Q

What is the in-phase power component?

A

Real, true, or active power (P) in watts

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26
Q

What is the out-of-phase power component?

A

Reactive power (Q) measured in vars

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27
Q

What is the additive result of active power and reactive power?

A

Apparent power (S) measured in VA

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28
Q

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?

A 
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)
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29
Q

What trig. function is related to finding total apparent power in a circuit?

A

Sin

30
Q

How does the relationship between sides of a triangle change from an impedance triangle to a power triangle of the same series circuit?

A

It does not. Relationships (pf) stay same

31
Q

What is the reference for a series phasor diagram, and why?

A

Current because it’s common to every circuit component.

32
Q

Where are the following volt drops drawn on a series phasor diagram:

1) Vr
2) V(XL)
3) V(XC)
4) V(coil)

A

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”

33
Q

When can you use impedance diagrams for parallel RLC circuits?

A

When solving INDIVIDUAL BRANCHES

34
Q

How do we find total current in a parallel RLC circuit?

A

1) phasor sum of all currents that flow through each branch

35
Q

How do we find total impedance in a parallel circuit?

A

Ztotal = E / Itotal (ohms law)

36
Q

What is the pf in parallel branch circuits with a resistor?

A

1; unity

37
Q

What is the impedance equal to in a parallel branch with only a resistor?

A

Impedance is equal to resistance.

Z(r) = R(r); straight horizontal line, pf = 1

38
Q

What is the pf in a parallel branch circuit with a capacitor?

A

0, 90° leading out-of-phase, straight vertical line

39
Q

What is the impedance equal to in a parallel branch with only a capacitor?

A

Capacitive reactance, Z(cap) = Xc, pf=0

40
Q

Once you have the total current of a parallel circuit, how do you find the overall pf?

A

Dividing in-phase component of current (x-axis) by the total current (phasorily added).

Ie. Adjacent/Hypotenuse = cos(theta) = pf

41
Q

What is the relationship between capacitors reactive power and coil reactive power?

A

180° out of phase

42
Q

How do you find total power of a parallel circuit?

A

Sum the power of the individual branches

43
Q

What’s the power of a capacitor?

A

0W

44
Q

How do you calculate the total reactive power of a parallel circuit?

A

Sum the reactive power of the individual branches

45
Q

What is the reactive power of a resistor?

A

0var

46
Q

How do you calculate total apparent power of a parallel circuit?

A

S= square root of (total power squared + total reactive power squared)

S= E x I(total)

S = current squared x total impedance

47
Q

How do you find pf of a parallel circuit?

A 
Pf = power/ apparent power or
Pf= in-phase component of current/total current
48
Q

What is the reference for a parallel phasor diagram?

A

Voltage

49
Q

In a parallel phasor diagram, a phasor representing ___________ (leading or lagging) current is shown counter-clockwise from the reference voltage.

A

Leading

50
Q

What should a phasor diagram include?

A
  • Voltage reference
  • Current through each branch
  • phase angle of each branch
  • total circuit current
  • circuit phase angle
51
Q

How many line voltages are there in a 3-phase wye-connected circuit?

A
  1. Vab, Vbc, Vca.
52
Q

How many phase voltages are there in a 3-phase wye-connected circuit? Include subscript names.

A
  1. Van, Vbn, Vcn
53
Q

What is the relationship between phase and line voltages in a balanced wye-connected load? (magnitude and angle)

A

Line V is 1.732 times larger

Line V leads phase V by 30°

54
Q

What is the relationship between phase current and line current in a wye-connected load?

A

They are equal to eachother

55
Q

How do you find the magnitude of the neutral current in a for a wye-connected circuit?

A

Phasor sum of the three line currents

56
Q

What equations would you use to find the power components of a balanced three phase motor with a pf of 0.8lag?

A

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

57
Q

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

A

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°

58
Q

How would you find I(a) for an unbalanced delta connected load?

A

I(ab) + I(ac)

59
Q

In a balanced three-phase delta-connected load, the line current is always ________ larger than its phase currents

A

1.732 times

60
Q

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?

A

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

61
Q

Where is I(ab)? No lag

A

0°

62
Q

Where is I(ba)? No lag

A

180°

63
Q

Where is I(bc)? No lag

A

240°

64
Q

Where is I(cb)? No lag.

A

60° (240-180)

65
Q

Where is I(ca)? No lag.

A

120°

66
Q

Where is I(ac)? No lag

A

300° (120-180)

67
Q

How do you determine the phase values of power in a balanced three-phase circuit, given the total power components?

A

Devide total power component by 3

68
Q

How do you find the total power components of a balanced multi-load three-phase system?

A

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)

69
Q

Compare the power dissipated by a delta-connected load vs. that same load connected in wye.

A

Power dissipated in delta is 3 times larger

70
Q

How can wye and dela supply the same apparent power (if each is connected to the same source)?

A

Wye supplies higher voltage at lower current, while delta supplies higher current at lower voltage.

71
Q

What is the line current of an alternator with a maximum of 100A per phase connected in:
A)delta
B)wye

A

A)173A

B)100A

72
Q

What happens to the output line voltage when a three-phase alternator is reconnected from a wye to a delta?

A

It is reduced by 1.73

4th Year Electrical (24 decks)

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