Formulas

Question 1

Ohm’s law

Answer 1

𝑉 = 𝐼𝑅

𝐼 = 𝑉 / 𝑅

𝑅 = 𝑉 / 𝐼

Question 2

Kirchhoff’s current law

Answer 2

𝚺 𝐼 = 0

Question 3

Kirchhoff’s voltage law

Answer 3

𝚺 𝑉 = 0

Question 4

frequency of a waveform

Answer 4

𝑓 = 1 / 𝑇

Question 5

sinusoidal voltage waveform

Answer 5

𝑣 = 𝑉ₚ sin 𝜃 = 𝑉ₚ sin 𝜔𝑡 = 𝑉ₚ sin 2𝜋𝑓𝑡

Question 6

angular frequency

Answer 6

𝜔 = 2𝜋𝑓 rad/s

Question 7

phase angle of a waveform at a particular point 𝜃

Answer 7

𝜃 = 𝜔𝑡 rad

Question 8

sinusoidal current waveform

Answer 8

𝑖 = 𝐼ₚ sin 𝜔𝑡 = 𝐼ₚ sin 2𝜋𝑓𝑡

Question 9

phase angle of a sinusoidal waveform

Answer 9

𝑦 = 𝐴 sin(𝜔𝑡 + 𝜑)

𝐴 = peak value of the waveform
𝜑 = phase angle of waveform at 𝑡 = 0

Question 10

average magnitude of a voltage waveform independent of its polarity

Answer 10

𝑉av = 2/𝜋 x 𝑉ₚ = 0.637 x 𝑉ₚ

Question 11

average magnitude of a current waveform independent of its polarity

Answer 11

𝐼av = 2/𝜋 x 𝐼ₚ = 0.637 x 𝐼ₚ

Question 12

r.m.s value of a sinusoidal voltage waveform

Answer 12

𝑉rms = 1/√2 x 𝑉ₚ = 0.707 x 𝑉ₚ

Question 13

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

Answer 13

𝐼rms = 1/√2 x 𝐼ₚ = 0.707 x 𝐼ₚ

Question 14

average power

Answer 14

𝑃av = (𝑉rms)(𝐼rms)

𝑃av = 𝑉²rms/𝑅

𝑃av = (𝐼²rms)(𝑅)

Question 15

power dissipated in a resistor

Answer 15

𝑃 = 𝑉𝐼

𝑃 = 𝐼²𝑅

𝑃 = 𝑉²/𝑅

Question 16

instantaneous power

Answer 16

𝑝 = 𝑣𝑖

𝑝 = 𝑖²𝑅

𝑝 = 𝑣²/𝑅

Question 17

form factor (general)

Answer 17

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

Question 18

peak factor (general)

Answer 18

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

Question 19

form factor of a sine wave

Answer 19

form factor = 0.707𝑉ₚ/0.637𝑉ₚ = 1.11

Question 20

peak factor of a sine wave

Answer 20

peak factor = 𝑉ₚ/0.707𝑉ₚ = 1.414

Question 21

peak factor of a square wave

Answer 21

peak factor = 1.0

Question 22

form factor of a square wave

Answer 22

form factor = 1.0

Question 23

phase difference

Answer 23

phase difference 𝜑 = 𝑡/𝑇 x 360° = 𝑡/𝑇 x 2𝜋 radians

Question 24

electric current

Answer 24

𝐼 = d𝑄 / d𝑡

Question 25

electric charge of an alternating current

Answer 25

𝑄 = ∫ 𝐼 d𝑡

Question 26

charge passed as the result of a flow of constant current

Answer 26

𝑄 = 𝐼 x 𝑡

Question 27

resistors in series

Answer 27

𝑅 = 𝑅1 + 𝑅2 + … + 𝑅n

Question 28

resistors in parallel

Answer 28

𝑅 = 1/[(1/𝑅1) + (1/𝑅2) + … + (1/𝑅n)]

Question 29

two resistors in parallel

Answer 29

𝑅 = (𝑅1𝑅2) / (𝑅1 + 𝑅2)

Question 30

parallel circuit composed of 𝑛 resistors of the same valur

Answer 30

𝑅 = 𝑅/𝑛

Question 31

relationship between open-circuit voltage and short-circuit current

Answer 31

𝑅 = 𝑉oc / 𝐼sc

Question 32

short-circuit current

Answer 32

𝐼sc = 𝑉oc / 𝑅

Question 33

open-circuit voltage

Answer 33

𝑉oc = 𝐼sc𝑅

Question 34

capacitance

Answer 34

𝐶 = 𝑄 / 𝑉 = 𝜀𝐴 / 𝑑 = 𝜀₀𝜀ᵣ𝐴 / 𝑑

Question 35

permittivity

Answer 35

𝜀 = 𝜀₀𝜀ᵣ = 𝐷 / 𝐸

Question 36

electric field strength

Answer 36

𝐸 = 𝑉 / 𝑑

Question 37

electric flux density

Answer 37

𝐷 = 𝑄 / 𝐴

Question 38

capacitors in parallel

Answer 38

𝐶 = 𝐶1 + 𝐶2 + … 𝐶n

Question 39

capacitors in series

Answer 39

𝐶 = 1/[(1/𝐶1) + (1/𝐶2) + … + (1/𝐶n)]

Question 40

voltage across a capacitor

Answer 40

𝑉 = 𝑄 / 𝐶 = 1 / 𝐶 ∫ 𝐼 d𝑡

Question 41

current through a capacitor

Answer 41

𝐼 = 𝐶 d𝑉/d𝑡

Question 42

time constant

Answer 42

Τ = 𝐶𝑅

Question 43

energy stored in a capacitor

Answer 43

𝐸 = ∫ [𝑉, 0] 𝐶𝑉 d𝑉 = 1/2𝐶𝑉²

Question 44

magnetic field strength in a wire

Answer 44

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

Question 45

magnetic flux density

Answer 45

𝐵 = 𝜱/𝐴 = 𝜇𝐻 = 𝜇₀𝜇ᵣ𝐻

Question 46

permeability

Answer 46

𝜇 = 𝜇₀𝜇ᵣ

Question 47

magnetomotive force

Answer 47

𝐹 = 𝐼𝑁 𝑁 = number of turns in the coil

Question 48

magnetic field strength in a coil with 𝑁 turns

Answer 48

𝐻 = 𝐼𝑁/𝑙 𝑙 = length of the flux path

Question 49

reluctance of a magnetic circuit

Answer 49

𝑆 = 𝐹/𝜱

Question 50

voltage induced in a conductor by a changing magnetic flux

Answer 50

𝑉 = 𝑁d𝜱/d𝑡

Question 51

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

Answer 51

𝑉 = 𝐿d𝐼/d𝑡

Question 52

inductance of a helical air-filled coil

Answer 52

𝐿 = (𝜇₀𝐴𝑁²)/𝑙 𝐴 = cross-sectional area 𝑙 = length

Question 53

inductance of a coil wound around a magnetic toroid

Answer 53

𝐿 = (𝜇₀𝜇ᵣ𝐴𝑁²)/𝑙 𝜇ᵣ = relative permeability of the material used for the toroid 𝐴 = cross-sectional area 𝑙 = length

Question 54

inductance of a coil wound around a nonmagnetic toroid

Answer 54

𝐿 = (𝜇₀𝐴𝑁²)/𝑙 𝐴 = cross-sectional area 𝑙 = length

Question 55

energy stored by an inductor

Answer 55

stored energy = (1/2)(𝐿𝐼²)

Question 56

mutual inductance

Answer 56

𝑉₂ = 𝑀d𝐼₁/d𝑡

Question 57

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

Answer 57

𝑉₂/𝑉₁ = 𝑁₂/𝑁₁

Question 58

efficiency of an ideal transformer

Answer 58

𝑉₁𝐼₁ = 𝑉₂𝐼₂

Question 59

sinusoidal voltage through a resistor

Answer 59

𝑣 = 𝐼ₚ𝑅 sin(𝜔𝑡)

Question 60

sinusoidal voltage through an inductor

Answer 60

𝑣 = 𝐿d(𝐼ₚ sin(𝜔𝑡))/d𝑡 = 𝜔𝐿𝐼ₚ cos(𝜔𝑡)

Question 61

sinusoidal voltage through a capacitor

Answer 61

𝑣 = (1/𝐶) ∫ 𝐼ₚ sin(𝜔𝑡)/d𝑡 = –(𝐼ₚ/𝜔𝐶) cos(𝜔𝑡)

Question 62

reactance of an inductor

Answer 62

𝑋 = 𝜔𝐿

Question 63

reactance of a capacitor

Answer 63

𝑋 = 1/𝜔𝐶

Question 64

impedances in series

Answer 64

𝑍 = 𝑍1 + 𝑍2 + … + 𝑍n

Question 65

impedances in parallel

Answer 65

1/𝑍 = 1/𝑍1 + 1/𝑍2 + … + 1/𝑍n

Question 66

power in an AC circuit

Answer 66

𝑝 = 𝑣𝑖

Question 67

AC power in a capacitor

Answer 67

𝑝 = 𝑉ₚ𝐼ₚ((sin 2𝜔𝑡)/2)

Question 68

AC power in an inductor

Answer 68

𝑝 = –𝑉ₚ𝐼ₚ((sin 2𝜔𝑡)/2)

Question 69

instaneous power in circuits with resistance and reactance

Answer 69

𝑝 = (1/2)𝑉ₚ𝐼ₚ cos 𝜑 – (1/2)𝑉ₚ𝐼ₚ cos (2𝜔𝑡 – 𝜑)

Question 70

active power

Answer 70

𝑃 = 𝑉𝐼 cos 𝜑 expressed in watts (W) 𝑉, 𝐼 are r.m.s. values of voltage and current

Question 71

power factor

Answer 71

power factor = active power (in watts) / apparent power (in volt amperes) = 𝑃/𝑆 = cos 𝜑

Question 72

reactive power

Answer 72

𝑄 = 𝑉𝐼 sin 𝜑

Question 73

apparent power

Answer 73

𝑆 = 𝑉𝐼

Question 74

relationship between apparent power, active power and reactive power

Answer 74

𝑆² = 𝑃² + 𝑄²

Question 75

voltage gain

Answer 75

𝐴ᵥ = 𝑉ₒ/𝑉ᵢ

Question 76

current gain

Answer 76

𝐴ᵢ = 𝐼ₒ/𝐼ᵢ

Question 77

power gain

Answer 77

𝐴ₚ = 𝑃ₒ/𝑃ᵢ

Question 78

power gain in decibels

Answer 78

power gain (dB) = 10 log₁₀ (𝑃₂/𝑃₁)

Question 79

voltage gain in decibels

Answer 79

voltage gain (dB) = 20 log₁₀ (𝑉₂/𝑉₁)

Question 80

the relationship between simple power gain and power gain in decibels

Answer 80

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

Question 81

the relationship between simple voltage gain and voltage gain in decibels

Answer 81

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

Question 82

transfer function of a circuit

Answer 82

𝑣ₒ/𝑣ᵢ = 𝐙₂/(𝐙₁+ 𝐙₂)

Question 83

transfer function of a high pass RC network

Answer 83

𝑣ₒ/𝑣ᵢ = 𝐙r/(𝐙r+ 𝐙c) = 𝑅/(𝑅 – j(1/𝜔𝐶) = 1/(1 – j(1/𝜔𝐶𝑅)

Question 84

angular cut-off frequency (RC network)

Answer 84

𝜔c = 1/𝐶𝑅 = 1/Τ rad/s

Question 85

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

Answer 85

𝑣ₒ/𝑣ᵢ = 1/(1 – j(𝑓c/𝑓)

Question 86

cyclic cut-off frequency (RC network)

Answer 86

𝑓c = 𝜔c/2𝜋 = 1/(2𝜋𝐶𝑅) Hz

Question 87

transfer function of a low-pass RC network

Answer 87

𝑣ₒ/𝑣ᵢ = 𝐙c/(𝐙r+ 𝐙c) = 1/(1 + j𝜔𝐶𝑅)

Question 88

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

Answer 88

𝑣ₒ/𝑣ᵢ = 1/(1 + j(𝑓c/𝑓)

Question 89

transfer function of a low-pass RL network

Answer 89

𝑣ₒ/𝑣ᵢ = 𝐙r/(𝐙r+ 𝐙L) = 𝑅/(𝑅 + j𝜔𝐿) = 1/(1 + j𝜔𝐿/𝑅)

Question 90

angular cut-off frequency (RL network)

Answer 90

𝜔c = 𝑅/𝐿 = 1/Τ rad/s

Question 91

transfer function of a high-pass RL network

Answer 91

𝑣ₒ/𝑣ᵢ = 𝐙L/(𝐙L + 𝐙r) = j𝜔𝐿/(𝑅 + j𝜔𝐿) = 1/(1 – j𝑅/𝜔𝐿)

Question 92

voltage across a resistor (series RLC circuit)

Answer 92

𝑣R = 𝑣 x 𝐙R/(𝐙R + 𝐙L + 𝐙c) = 𝑣 x 𝑅/(𝑅 + j𝜔𝐿 + 1/(j𝜔𝐿))

Question 93

impedance of a series RLC network

Answer 93

𝐙 = 𝑅 + j𝜔𝐿 + 1/(j𝜔𝐶) = 𝑅 + j(𝜔𝐿 – 1/(𝜔𝐶))

Question 94

angular resonant frequency

Answer 94

𝜔₀ = 1/√(𝐿𝐶)

Question 95

cyclic resonant frequency

Answer 95

𝑓₀ = 1/(2𝜋√(𝐿𝐶))

Question 96

quality factor of a series resonant circuit

Answer 96

𝑄 = 𝑋/𝑅 = 𝑉/𝑉ᵣ = (1/𝑅)(√(𝐿𝐶)) 𝑋 and 𝑉 can be the quantity associated with either the capacitor or the inductor (because they store an equal amount of energy)

Question 97

relationship between resonant frequency and bandwidth

Answer 97

𝑄 = 𝑓₀/𝐵 𝐵 = bandwidth

Question 98

bandwidth of a circuit

Answer 98

𝐵 = 𝑅/(2𝜋𝐿) Hz

Question 99

impedance of a parallel RLC network

Answer 99

𝐙 = 1/((1/𝑅) + j𝜔𝐶 + 1/(j𝜔𝐿) = 1/(𝑅 + jj𝜔𝐶 – 1/(𝜔𝐿))

Question 100

quality factor of a parallel resonant circuit

Answer 100

𝑄 = 𝑋/𝑅 = 𝑉/𝑉ᵣ = (𝑅)(√𝐶/𝐿)