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Formulas Flashcards

1
Q

Ohm’s law

A

𝑉 = 𝐼𝑅

𝐼 = 𝑉 / 𝑅

𝑅 = 𝑉 / 𝐼

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2
Q

Kirchhoff’s current law

A

𝚺 𝐼 = 0

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3
Q

Kirchhoff’s voltage law

A

𝚺 𝑉 = 0

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4
Q

frequency of a waveform

A

𝑓 = 1 / 𝑇

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5
Q

sinusoidal voltage waveform

A

𝑣 = π‘‰β‚š sin πœƒ = π‘‰β‚š sin πœ”π‘‘ = π‘‰β‚š sin 2πœ‹π‘“π‘‘

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6
Q

angular frequency

A

πœ” = 2πœ‹π‘“ rad/s

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7
Q

phase angle of a waveform at a particular point πœƒ

A

πœƒ = πœ”π‘‘ rad

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8
Q

sinusoidal current waveform

A

𝑖 = πΌβ‚š sin πœ”π‘‘ = πΌβ‚š sin 2πœ‹π‘“π‘‘

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9
Q

phase angle of a sinusoidal waveform

A

𝑦 = 𝐴 sin(πœ”π‘‘ + πœ‘)

𝐴 = peak value of the waveform
πœ‘ = phase angle of waveform at 𝑑 = 0

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10
Q

average magnitude of a voltage waveform independent of its polarity

A

𝑉av = 2/πœ‹ x π‘‰β‚š = 0.637 x π‘‰β‚š

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11
Q

average magnitude of a current waveform independent of its polarity

A

𝐼av = 2/πœ‹ x πΌβ‚š = 0.637 x πΌβ‚š

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12
Q

r.m.s value of a sinusoidal voltage waveform

A

𝑉rms = 1/√2 x π‘‰β‚š = 0.707 x π‘‰β‚š

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13
Q

r.m.s. value of a sinusoidal current waveform

A

𝐼rms = 1/√2 x πΌβ‚š = 0.707 x πΌβ‚š

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14
Q

average power

A

𝑃av = (𝑉rms)(𝐼rms)

𝑃av = 𝑉²rms/𝑅

𝑃av = (𝐼²rms)(𝑅)

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15
Q

power dissipated in a resistor

A

𝑃 = 𝑉𝐼

𝑃 = 𝐼²𝑅

𝑃 = 𝑉²/𝑅

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16
Q

instantaneous power

A

𝑝 = 𝑣𝑖

𝑝 = 𝑖²𝑅

𝑝 = 𝑣²/𝑅

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17
Q

form factor (general)

A

form factor = (r.m.s. value / average value)

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18
Q

peak factor (general)

A

peak factor = (peak value)/(r.m.s. value)

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19
Q

form factor of a sine wave

A

form factor = 0.707π‘‰β‚š/0.637π‘‰β‚š = 1.11

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20
Q

peak factor of a sine wave

A

peak factor = π‘‰β‚š/0.707π‘‰β‚š = 1.414

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21
Q

peak factor of a square wave

A

peak factor = 1.0

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22
Q

form factor of a square wave

A

form factor = 1.0

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23
Q

phase difference

A

phase difference πœ‘ = 𝑑/𝑇 x 360Β° = 𝑑/𝑇 x 2πœ‹ radians

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24
Q

electric current

A

𝐼 = d𝑄 / d𝑑

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25
Q

electric charge of an alternating current

A

𝑄 = ∫ 𝐼 d𝑑

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26
Q

charge passed as the result of a flow of constant current

A

𝑄 = 𝐼 x 𝑑

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27
Q

resistors in series

A

𝑅 = 𝑅1 + 𝑅2 + … + 𝑅n

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28
Q

resistors in parallel

A

𝑅 = 1/[(1/𝑅1) + (1/𝑅2) + … + (1/𝑅n)]

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29
Q

two resistors in parallel

A

𝑅 = (𝑅1𝑅2) / (𝑅1 + 𝑅2)

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30
Q

parallel circuit composed of 𝑛 resistors of the same valur

A

𝑅 = 𝑅/𝑛

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31
Q

relationship between open-circuit voltage and short-circuit current

A

𝑅 = 𝑉oc / 𝐼sc

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32
Q

short-circuit current

A

𝐼sc = 𝑉oc / 𝑅

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33
Q

open-circuit voltage

A

𝑉oc = 𝐼sc𝑅

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34
Q

capacitance

A

𝐢 = 𝑄 / 𝑉 = πœ€π΄ / 𝑑 = πœ€β‚€πœ€α΅£π΄ / 𝑑

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35
Q

permittivity

A

πœ€ = πœ€β‚€πœ€α΅£ = 𝐷 / 𝐸

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36
Q

electric field strength

A

𝐸 = 𝑉 / 𝑑

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37
Q

electric flux density

A

𝐷 = 𝑄 / 𝐴

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38
Q

capacitors in parallel

A

𝐢 = 𝐢1 + 𝐢2 + … 𝐢n

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39
Q

capacitors in series

A

𝐢 = 1/[(1/𝐢1) + (1/𝐢2) + … + (1/𝐢n)]

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40
Q

voltage across a capacitor

A

𝑉 = 𝑄 / 𝐢 = 1 / 𝐢 ∫ 𝐼 d𝑑

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41
Q

current through a capacitor

A

𝐼 = 𝐢 d𝑉/d𝑑

42
Q

time constant

A

Ξ€ = 𝐢𝑅

43
Q

energy stored in a capacitor

A

𝐸 = ∫ [𝑉, 0] 𝐢𝑉 d𝑉 = 1/2𝐢𝑉²

44
Q

magnetic field strength in a wire

A

𝐻 = 𝐼/𝑙

𝐼 = current flowing in the wire
𝑙 = length of the magnetic circuit

45
Q

magnetic flux density

A

𝐡 = 𝜱/𝐴 = πœ‡π» = πœ‡β‚€πœ‡α΅£π»

46
Q

permeability

A

πœ‡ = πœ‡β‚€πœ‡α΅£

47
Q

magnetomotive force

A

𝐹 = 𝐼𝑁

𝑁 = number of turns in the coil

48
Q

magnetic field strength in a coil with 𝑁 turns

A

𝐻 = 𝐼𝑁/𝑙

𝑙 = length of the flux path

49
Q

reluctance of a magnetic circuit

A

𝑆 = 𝐹/𝜱

50
Q

voltage induced in a conductor by a changing magnetic flux

A

𝑉 = 𝑁d𝜱/d𝑑

51
Q

the voltage produced across an inductor as a result of changes in the current

A

𝑉 = 𝐿d𝐼/d𝑑

52
Q

inductance of a helical air-filled coil

A

𝐿 = (πœ‡β‚€π΄π‘Β²)/𝑙

𝐴 = cross-sectional area
𝑙 = length

53
Q

inductance of a coil wound around a magnetic toroid

A

𝐿 = (πœ‡β‚€πœ‡α΅£π΄π‘Β²)/𝑙

πœ‡α΅£ = relative permeability of the material used for the toroid
𝐴 = cross-sectional area
𝑙 = length

54
Q

inductance of a coil wound around a nonmagnetic toroid

A

𝐿 = (πœ‡β‚€π΄π‘Β²)/𝑙

𝐴 = cross-sectional area
𝑙 = length

55
Q

energy stored by an inductor

A

stored energy = (1/2)(𝐿𝐼²)

56
Q

mutual inductance

A

𝑉₂ = 𝑀d𝐼₁/d𝑑

57
Q

ratio of a transformer’s output voltage to its input voltage

A

𝑉₂/𝑉₁ = 𝑁₂/𝑁₁

58
Q

efficiency of an ideal transformer

A

𝑉₁𝐼₁ = 𝑉₂𝐼₂

59
Q

sinusoidal voltage through a resistor

A

𝑣 = πΌβ‚šπ‘… sin(πœ”π‘‘)

60
Q

sinusoidal voltage through an inductor

A

𝑣 = 𝐿d(πΌβ‚š sin(πœ”π‘‘))/d𝑑 = πœ”πΏπΌβ‚š cos(πœ”π‘‘)

61
Q

sinusoidal voltage through a capacitor

A

𝑣 = (1/𝐢) ∫ πΌβ‚š sin(πœ”π‘‘)/d𝑑 = –(πΌβ‚š/πœ”πΆ) cos(πœ”π‘‘)

62
Q

reactance of an inductor

A

𝑋 = πœ”πΏ

63
Q

reactance of a capacitor

A

𝑋 = 1/πœ”πΆ

64
Q

impedances in series

A

𝑍 = 𝑍1 + 𝑍2 + … + 𝑍n

65
Q

impedances in parallel

A

1/𝑍 = 1/𝑍1 + 1/𝑍2 + … + 1/𝑍n

66
Q

power in an AC circuit

A

𝑝 = 𝑣𝑖

67
Q

AC power in a capacitor

A

𝑝 = π‘‰β‚šπΌβ‚š((sin 2πœ”π‘‘)/2)

68
Q

AC power in an inductor

A

𝑝 = β€“π‘‰β‚šπΌβ‚š((sin 2πœ”π‘‘)/2)

69
Q

instaneous power in circuits with resistance and reactance

A

𝑝 = (1/2)π‘‰β‚šπΌβ‚š cos πœ‘ – (1/2)π‘‰β‚šπΌβ‚š cos (2πœ”π‘‘ – πœ‘)

70
Q

active power

A

𝑃 = 𝑉𝐼 cos πœ‘

expressed in watts (W)

𝑉, 𝐼 are r.m.s. values of voltage and current

71
Q

power factor

A

power factor = active power (in watts) / apparent power (in volt amperes) = 𝑃/𝑆 = cos πœ‘

72
Q

reactive power

A

𝑄 = 𝑉𝐼 sin πœ‘

73
Q

apparent power

A

𝑆 = 𝑉𝐼

74
Q

relationship between apparent power, active power and reactive power

A

𝑆² = 𝑃² + 𝑄²

75
Q

voltage gain

A

𝐴α΅₯ = 𝑉ₒ/𝑉ᡒ

76
Q

current gain

A

𝐴ᡒ = 𝐼ₒ/𝐼ᡒ

77
Q

power gain

A

π΄β‚š = 𝑃ₒ/𝑃ᡒ

78
Q

power gain in decibels

A

power gain (dB) = 10 log₁₀ (𝑃₂/𝑃₁)

79
Q

voltage gain in decibels

A

voltage gain (dB) = 20 log₁₀ (𝑉₂/𝑉₁)

80
Q

the relationship between simple power gain and power gain in decibels

A

power gain = 10^(power gain(dB)/10)

81
Q

the relationship between simple voltage gain and voltage gain in decibels

A

voltage gain = 10^(voltage gain(dB)/20)

82
Q

transfer function of a circuit

A

𝑣ₒ/𝑣ᡒ = 𝐙₂/(𝐙₁+ 𝐙₂)

83
Q

transfer function of a high pass RC network

A

𝑣ₒ/𝑣ᡒ = 𝐙r/(𝐙r+ 𝐙c) = 𝑅/(𝑅 – j(1/πœ”πΆ) = 1/(1 – j(1/πœ”πΆπ‘…)

84
Q

angular cut-off frequency (RC network)

A

πœ”c = 1/𝐢𝑅 = 1/Ξ€ rad/s

85
Q

transfer function of a high-pass RC network expressed in terms of signal frequency and cut-off frequency

A

𝑣ₒ/𝑣ᡒ = 1/(1 – j(𝑓c/𝑓)

86
Q

cyclic cut-off frequency (RC network)

A

𝑓c = πœ”c/2πœ‹ = 1/(2πœ‹πΆπ‘…) Hz

87
Q

transfer function of a low-pass RC network

A

𝑣ₒ/𝑣ᡒ = 𝐙c/(𝐙r+ 𝐙c) = 1/(1 + jπœ”πΆπ‘…)

88
Q

transfer function of a low-pass RC network expressed in terms of signal frequency and cut-off frequency

A

𝑣ₒ/𝑣ᡒ = 1/(1 + j(𝑓c/𝑓)

89
Q

transfer function of a low-pass RL network

A

𝑣ₒ/𝑣ᡒ = 𝐙r/(𝐙r+ 𝐙L) = 𝑅/(𝑅 + jπœ”πΏ) = 1/(1 + jπœ”πΏ/𝑅)

90
Q

angular cut-off frequency (RL network)

A

πœ”c = 𝑅/𝐿 = 1/Ξ€ rad/s

91
Q

transfer function of a high-pass RL network

A

𝑣ₒ/𝑣ᡒ = 𝐙L/(𝐙L + 𝐙r) = jπœ”πΏ/(𝑅 + jπœ”πΏ) = 1/(1 – j𝑅/πœ”πΏ)

92
Q

voltage across a resistor (series RLC circuit)

A

𝑣R = 𝑣 x 𝐙R/(𝐙R + 𝐙L + 𝐙c) = 𝑣 x 𝑅/(𝑅 + jπœ”πΏ + 1/(jπœ”πΏ))

93
Q

impedance of a series RLC network

A

𝐙 = 𝑅 + jπœ”πΏ + 1/(jπœ”πΆ) = 𝑅 + j(πœ”πΏ – 1/(πœ”πΆ))

94
Q

angular resonant frequency

A

πœ”β‚€ = 1/√(𝐿𝐢)

95
Q

cyclic resonant frequency

A

𝑓₀ = 1/(2πœ‹βˆš(𝐿𝐢))

96
Q

quality factor of a series resonant circuit

A

𝑄 = 𝑋/𝑅 = 𝑉/𝑉ᡣ = (1/𝑅)(√(𝐿𝐢))

𝑋 and 𝑉 can be the quantity associated with either the capacitor or the inductor (because they store an equal amount of energy)

97
Q

relationship between resonant frequency and bandwidth

A

𝑄 = 𝑓₀/𝐡

𝐡 = bandwidth

98
Q

bandwidth of a circuit

A

𝐡 = 𝑅/(2πœ‹πΏ) Hz

99
Q

impedance of a parallel RLC network

A

𝐙 = 1/((1/𝑅) + jπœ”πΆ + 1/(jπœ”πΏ) = 1/(𝑅 + jjπœ”πΆ – 1/(πœ”πΏ))

100
Q

quality factor of a parallel resonant circuit

A

𝑄 = 𝑋/𝑅 = 𝑉/𝑉ᡣ = (𝑅)(√𝐢/𝐿)

Engineering (7 decks)

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