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Science > Electrical Systems - Formula - Level 3 > Flashcards

Electrical Systems - Formula - Level 3 Flashcards

1
Q

Charge

A

Symbol - Q

Unit - Coulombs (C)

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2
Q

Capacitance

A

Symbol - C
Unit - Farads (F),
1 farad = 1 coulomb per volt

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3
Q

Voltage

A

Symbol - V

Unit - Volts (V)

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4
Q

Permittivity of free space

A

Symbol - Ɛo

Unit - Farad per meter (Fm^-1)

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5
Q

Dielectric constant

A

Symbol - Ɛr

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6
Q

Area of plate

A

Symbol - A

Unit - Square meters (m^2)

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7
Q

Potential energy

A

Symbol - Ep

Unit - Joules (J)

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8
Q

Time constant

A

Symbol - T

Unit - Seconds (s)

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9
Q

Resistance

A

Symbol - R

Unit - Ohms (Ω)

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10
Q

Distance between plates

A

Symbol - d

Unit - Meters (m)

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11
Q

Magnetic flux

A

Symbol - Φ

Unit - Webers (Wb)

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12
Q

Magnetic field strength

A

Symbol - B

Unit - Teslas (T) or Weber per square meter (Wb m^-2)

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13
Q

Electromotive force (EMF)

A

Symbol - E

Unit - Volts (V)

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14
Q

Inductance

A

Symbol - L

Unit - Henrys (H)

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15
Q

Current

A

Symbol - I

Unit - Amps (A)

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16
Q

Time

A

Symbol - t

Unit - Seconds (s)

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17
Q

Mutual inductance

A

Symbol - M
Unit - Henrys (H)

M is a constant which depends on…

  1. The size of the coils
  2. The distance between the two coils
  3. The material inside the two coils
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18
Q

Alternating voltage

A

Symbol - Vp

Unit - Volts (V)

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19
Q

Number of turns on primary coil

A

Symbol - Np

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20
Q

Number of turns on secondary coil

A

Symbol - Ns

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21
Q

Voltage across secondary coil

A

Symbol - Vs

Units - Volts (V)

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22
Q

Angular frequency

A

Symbol - ω

Units - Radians per second (s^-1)

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23
Q

Power

A

Symbol - P

Units - Watts (W) or Joules per second (Js^-1)

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24
Q

Peak current

A

Symbol - Imax

Units - Amps (A)

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25
Q

Peak voltage

A

Symbol - Vmax

Units - Volts (V)

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26
Q

Root mean square current

A

Symbol - Irms

Units - Amps (A)

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27
Q

Root mean square voltage

A

Symbol - Vrms

Units - Volts (V)

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28
Q

Reactance of a capacitor

A

Symbol - Xc

Units - Ohms (Ω)

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29
Q

Reactance of an inductor

A

Symbol - Xl

Units - Ohms (Ω)

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30
Q

Impedance

A

Symbol - Z

Units - Ohms (Ω)

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31
Q

Frequency

A

Symbol - f

Units - Hertz (Hz)

32
Q

Equation for mutual inductance

A

Φs = MIp

Where,
Φs is the magnetic flux in the secondary coil (S)
M is the mutual inductance constant
Ip is the induced voltage in the primary coil (P)

33
Q

Equation for Faraday’s law of mutual inductance

A

Vs = -M(△I)/△t)p

Where,
Vs is the induced voltage,
M is the mutual inductance constant
Ip is the maximum current in the primary coil (P)
t is the time taken to go from 0 to the maximum current in the primary coil (P) after the switch has been turned on

  • Negative sign indicates that the induced voltage in the secondary coil (Vs) opposes the changing current in the primary coil (Ip).
34
Q

Equation for transformer

A

Vp/Vs = Np/Ns = Is/Ip

Where,
Vp is the induced voltage in the primary coil
Vs is the induced voltage in the secondary coil
Np is the number of turns of the primary coil
Ns is the number of turns of the secondary coil
Is is the induced current in the secondary coil
Ip is the induced current in the primary coil

35
Q

Equation for ideal transformer

A

Vp Ip = Vs Is

Where,
Vp is the induced voltage in the primary coil (P)
Ip is the maximum current in the primary coil (P)
Vs is the induced voltage in the secondary coil (S)
Is is the current in the secondary coil (S)

36
Q

Equation for magnitude of magnetic field through an area A, perpendicular to a magnetic field B

A

Φ = BA

Where,
Φ is the magnetic flux
A is the area
B is the magnetic field strength (flux density)

37
Q

Equation for power dissipated by a resistor

A

P = IV = I^2R = V^2/R

Where, 
P is the power
V is the voltage
I is the current
R is the resistance
38
Q

Equation for number of turns of coil

A

V = -NBAω sinωt

Where, 
V is the supply voltage
N is the number of turns
B is the magnetic field strength
A is the area 
ω is the angular velocity of the coil
39
Q

Equation for maximum and minimum voltage of A.C. current in generator

A

Vmax = NBAω

Where,
N is the number of turns
B is the magnetic field strength
A is the area

Vmin = 0

40
Q

Equation for efficiency of a transformer

A

Ef = VsIs / VpIp x 100

41
Q

Equation for self-inductance of a coil

A

V = -L △I/△t

Where,
V is the opposing induced voltage (Faraday’s law)
L is the self-inductance of the coil (constant)
I is the opposing induced current

  • Negative sign indicates that the induced voltage opposes the change of current (lenz law).
42
Q

Equation for opposing induced voltage (Faraday’s law)

A

V = -△Φ/△t

Where,
V is the opposing induced voltage (Faraday’s law)
Φ is the magnetic flux in the coil

43
Q

Equation for energy stored in an inductor

A

E = 1/2 LI^2

Where,
E is the energy stored in the inductor
L is the self-inductance of the coil
I is the opposing induced current

44
Q

Equation for time constant

A

τ = L/R

Where,
τ is the time constant
L is the self-inductance of the coil
R is the resistance of the coil

45
Q

Equation for maximum current

A

I = V/R

Where,
I is the maximum current
V is the voltage of the source
R is the total resistance

46
Q

Equation for capacitance from charge and voltage

A

C = Q/V

Where,
C is the capacitance of a capacitor (constant)
Q is the charge of each plate when connected across a supply
V is the voltage of the supply

47
Q

Equation for capacitance of a capacitor

A

C = (εr εo A)/d

Where,
C is the capacitance of a capacitor (constant)
εr is the dielectric constant of the insulation (if any)
εo is the absolute permittivity of free space (air/vacuum)
A is the area of the plates
d is the distance between the plates

48
Q

Equation for capacitance and charge in series

A
  • Capicatances of each capacitor inversed adds up to the inverse of the total capacitance
    1/Cs = 1/C1 + 1/C2
  • Charge is the same for each capacitor in the series circuit
49
Q

Equation for capacitance and charge in parallel

A
  • Capacitance of each capacitor adds up to the total capacitance of the circuit
    Cp = C1 + C2
  • Charge of each capacitor adds up to the total charge stored
    Q = Q1 + Q2
50
Q

Equation for energy stored by a capacitor from capacitance and charge

A

Ep = 1/2 x q^2/C

Where,
Ep is the potential energy stored in the capacitor
q is the charge stored by the capacitor
C is the capacitance

  • Energy is also given by the area under a graph of V/q
51
Q

Equation for energy stored by a capacitor from voltage and charge

A

Ep = 1/2 x qV

Where,
Ep is the potential energy stored in the capacitor
q is the charge stored by the capacitor
V is the voltage of the capacitor

  • Energy is also given by the area under the graph of V/q, which is a straight line through (0,0)
52
Q

Equation for charging and discharging current of capacitor

A

At any instant, Vs = Vc + VR

Where,
Vs is the voltage of the source
Vc is the voltage of the capacitor
VR is the voltage of the resistor

53
Q

Equation for strength of electric field between two oppositely charged capacitor plates

A

E = V/d

Where,
E is the strength of electric field between the plates
d is the distance between the plates
V is the potential difference across the plates

54
Q

Equation for energy provided by a cell

A

E = qV

Where,
E is the energy provided by the cell
q is the charge from the cell
V is the change in energy per unit charge

  • Energy is also given by the area under the graph of V/q, which is a straight horizontal line
55
Q

Equation for energy stored by a capacitor from capacitance and voltage

A

Ep = 1/2 x C x V^2

Where,
Ep is the potential energy stored in the capacitor
C is the capacitance
V is the voltage of the capacitor

56
Q

Converting from mA to A

A

mA / 1000 = A

57
Q

Equations for current, voltage and resistance in a series circuit

A
  • Current is the same for each component in the series circuit
  • Voltages of each component add up to the supply voltage
    V = V1 + V2
  • Resistances of each resistor add up to the total resistance
    Rs = R1 + R2
58
Q

Equations for current, voltage and resistance in a parallel circuit

A
  • Currents of each component add up to the supply current
    I = I1 + I2
  • Voltage is the same for each component in the parallel circuit
  • Resistances of each resistor inversed adds up to the inverse of the total resistance
    1/Rp = 1/R1 + 1/R2
59
Q

Equation for time constant

A

τ = RC

Where,
τ is the time constant
R is the resistance of the circuit
C is the capacitance of the circuit

60
Q

Equation for charge on a capacitor

A

Q = VC

Where,
Q is the charge on a capacitor at any instant in time
V is the voltage of the capacitor
C is the capacitance of the capacitor

(Capacitance is constant - thus charge and voltage are directly proportional)

61
Q

Equation for energy stored Equation for energy stored by a capacitor from capacitance and voltage

A

Ep = 1/2 x CV^2

Where,
Ep is the potential energy stored in the capacitor
C is the capacitance of the capacitor
V is the voltage of the capacitor

62
Q

Equation for the induced voltage in a loop pushed into a magnetic field (entering magnetic flux)

A

V = BvL

Where, 
V is the size of the induced voltage
B is the magnetic field strength, 
v is the speed of movement across the field lines 
L is the length of the wire in the field
63
Q

Equation for rate of change of flux

A

V = -N△ϕ / t

Where, 
V is the induced voltage,
N is the number of turns in the coil 
△ϕ is the change in flux,
t is the time taken for the flux to change
  • The negative sign indicates that the induced current causes a force to oppose the change which produces it.
64
Q

Equations for an ideal transformer

A 
Vs/Vp = Ns/Np
VpIp = VsIs
  • If the whole of the magnetic flux produced in the primary coil (MIp) is converted to the induced voltage in the secondary coil (Vs), it is an ideal transformer.
65
Q

Equations for resonance

A

XL = XC

2π fo L = 1 / 2π fo C

Where, 
XL is the reactance of the inductor
XC is the reactance of the capacitor
fo is the resonant frequency 
L is the inductance 
C is the capacitance
66
Q

Equation for the supply voltage from current and impedance

A

Vs = IZ

Where,
Vs is the supply voltage
I is the current
Z is the impedance

67
Q

Equation for the impedance from resistance and reactance

A

Z = √R^2 + XL^2

Where,
Z is the impedance
R is the resistance
XL is the reactance of the inductor

68
Q

Equation for the energy stored in an inductor

A

E = 1/2 LI^2

Where,
E is the energy stored in an inductor
L is the inductance of the wire
I is the current of the wire

69
Q

Equation for the time constant

A

τ = L/R

Where,
τ is the time constant
L is the inductance of the inductor
R is the resistance in the circuit

70
Q

Equation for the changing voltage in an AC circuit

A

V = Vmax sin ωt

Where, 
V is the voltage of the AC circuit
Vmax is the maximum voltage 
ω is the angular speed of the rotation of the generator coil 
t is the time
71
Q

Equation for the changing current in an AC circuit

A

I = Imax sin ωt

Where, 
I is the current of the AC circuit
Imax is the maximum current
ω is the angular speed of the rotation of the generator coil 
t is the time
72
Q

Equation for the root mean square current and voltage

A 
Irms = Imax / √2
Vrms = Vmax / √2
Where, 
Irms is the root mean squared current
Imax is the maximum current
Vrms is the root mean squared voltage
Vmax is the maximum voltage
73
Q

Equation for the reactance of a capacitor from current

A

Xc = Vc/I

Where,
Xc is the reactance of the capacitor
Vc is the voltage of the capacitor
I is the current

74
Q

Equation for the reactance of a capacitor from frequency

A

Xc = 1/2πfC

Where,
Xc is the reactance of the capacitor
2πf is the angular velocity
C is the capacitance of the capacitor

75
Q

Equation for the reactance of an inductor from frequency

A

Xl = 2πfL

Where,
Xl is the reactance of the inductor
2πf is the angular velocity
C is the capacitance of the capacitor

76
Q

Voltage relationships at resonance

A

At resonance Xl = Xc,
thus Vl = Vc

At resonance Z = R
thus Vs = Vr = IR

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