Electrical Systems - Formula - Level 3 Flashcards
(76 cards)
1
Q
Charge
A
Symbol - Q
Unit - Coulombs (C)
2
Q
Capacitance
A
Symbol - C
Unit - Farads (F),
1 farad = 1 coulomb per volt
3
Q
Voltage
A
Symbol - V
Unit - Volts (V)
4
Q
Permittivity of free space
A
Symbol - Ɛo
Unit - Farad per meter (Fm^-1)
5
Q
Dielectric constant
A
Symbol - Ɛr
6
Q
Area of plate
A
Symbol - A
Unit - Square meters (m^2)
7
Q
Potential energy
A
Symbol - Ep
Unit - Joules (J)
8
Q
Time constant
A
Symbol - T
Unit - Seconds (s)
9
Q
Resistance
A
Symbol - R
Unit - Ohms (Ω)
10
Q
Distance between plates
A
Symbol - d
Unit - Meters (m)
11
Q
Magnetic flux
A
Symbol - Φ
Unit - Webers (Wb)
12
Q
Magnetic field strength
A
Symbol - B
Unit - Teslas (T) or Weber per square meter (Wb m^-2)
13
Q
Electromotive force (EMF)
A
Symbol - E
Unit - Volts (V)
14
Q
Inductance
A
Symbol - L
Unit - Henrys (H)
15
Q
Current
A
Symbol - I
Unit - Amps (A)
16
Q
Time
A
Symbol - t
Unit - Seconds (s)
17
Q
Mutual inductance
A
Symbol - M
Unit - Henrys (H)
M is a constant which depends on…
- The size of the coils
- The distance between the two coils
- The material inside the two coils
18
Q
Alternating voltage
A
Symbol - Vp
Unit - Volts (V)
19
Q
Number of turns on primary coil
A
Symbol - Np
20
Q
Number of turns on secondary coil
A
Symbol - Ns
21
Q
Voltage across secondary coil
A
Symbol - Vs
Units - Volts (V)
22
Q
Angular frequency
A
Symbol - ω
Units - Radians per second (s^-1)
23
Q
Power
A
Symbol - P
Units - Watts (W) or Joules per second (Js^-1)
24
Q
Peak current
A
Symbol - Imax
Units - Amps (A)
25
Peak voltage
Symbol - Vmax
| Units - Volts (V)
26
Root mean square current
Symbol - Irms
| Units - Amps (A)
27
Root mean square voltage
Symbol - Vrms
| Units - Volts (V)
28
Reactance of a capacitor
Symbol - Xc
| Units - Ohms (Ω)
29
Reactance of an inductor
Symbol - Xl
| Units - Ohms (Ω)
30
Impedance
Symbol - Z
| Units - Ohms (Ω)
31
Frequency
Symbol - f
| Units - Hertz (Hz)
32
Equation for mutual inductance
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
Equation for Faraday's law of mutual inductance
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
Equation for transformer
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
Equation for ideal transformer
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
Equation for magnitude of magnetic field through an area A, perpendicular to a magnetic field B
Φ = BA
Where,
Φ is the magnetic flux
A is the area
B is the magnetic field strength (flux density)
37
Equation for power dissipated by a resistor
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
Equation for number of turns of coil
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
Equation for maximum and minimum voltage of A.C. current in generator
Vmax = NBAω
Where,
N is the number of turns
B is the magnetic field strength
A is the area
Vmin = 0
40
Equation for efficiency of a transformer
Ef = VsIs / VpIp x 100
41
Equation for self-inductance of a coil
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
Equation for opposing induced voltage (Faraday's law)
V = -△Φ/△t
Where,
V is the opposing induced voltage (Faraday's law)
Φ is the magnetic flux in the coil
43
Equation for energy stored in an inductor
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
Equation for time constant
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
Equation for maximum current
I = V/R
Where,
I is the maximum current
V is the voltage of the source
R is the total resistance
46
Equation for capacitance from charge and voltage
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
Equation for capacitance of a capacitor
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
Equation for capacitance and charge in series
- 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
Equation for capacitance and charge in parallel
- 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
Equation for energy stored by a capacitor from capacitance and charge
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
Equation for energy stored by a capacitor from voltage and charge
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
Equation for charging and discharging current of capacitor
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
Equation for strength of electric field between two oppositely charged capacitor plates
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
Equation for energy provided by a cell
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
Equation for energy stored by a capacitor from capacitance and voltage
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
Converting from mA to A
mA / 1000 = A
57
Equations for current, voltage and resistance in a series circuit
- 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
Equations for current, voltage and resistance in a parallel circuit
- 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
Equation for time constant
τ = RC
Where,
τ is the time constant
R is the resistance of the circuit
C is the capacitance of the circuit
60
Equation for charge on a capacitor
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
Equation for energy stored Equation for energy stored by a capacitor from capacitance and voltage
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
Equation for the induced voltage in a loop pushed into a magnetic field (entering magnetic flux)
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
Equation for rate of change of flux
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
Equations for an ideal transformer
```
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
Equations for resonance
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
Equation for the supply voltage from current and impedance
Vs = IZ
Where,
Vs is the supply voltage
I is the current
Z is the impedance
67
Equation for the impedance from resistance and reactance
Z = √R^2 + XL^2
Where,
Z is the impedance
R is the resistance
XL is the reactance of the inductor
68
Equation for the energy stored in an inductor
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
Equation for the time constant
τ = L/R
Where,
τ is the time constant
L is the inductance of the inductor
R is the resistance in the circuit
70
Equation for the changing voltage in an AC circuit
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
Equation for the changing current in an AC circuit
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
Equation for the root mean square current and voltage
```
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
Equation for the reactance of a capacitor from current
Xc = Vc/I
Where,
Xc is the reactance of the capacitor
Vc is the voltage of the capacitor
I is the current
74
Equation for the reactance of a capacitor from frequency
Xc = 1/2πfC
Where,
Xc is the reactance of the capacitor
2πf is the angular velocity
C is the capacitance of the capacitor
75
Equation for the reactance of an inductor from frequency
Xl = 2πfL
Where,
Xl is the reactance of the inductor
2πf is the angular velocity
C is the capacitance of the capacitor
76
Voltage relationships at resonance
At resonance Xl = Xc,
thus Vl = Vc
At resonance Z = R
thus Vs = Vr = IR
