Electrical Systems - Formula - Level 3 Flashcards
Charge
Symbol - Q
Unit - Coulombs (C)
Capacitance
Symbol - C
Unit - Farads (F),
1 farad = 1 coulomb per volt
Voltage
Symbol - V
Unit - Volts (V)
Permittivity of free space
Symbol - Ɛo
Unit - Farad per meter (Fm^-1)
Dielectric constant
Symbol - Ɛr
Area of plate
Symbol - A
Unit - Square meters (m^2)
Potential energy
Symbol - Ep
Unit - Joules (J)
Time constant
Symbol - T
Unit - Seconds (s)
Resistance
Symbol - R
Unit - Ohms (Ω)
Distance between plates
Symbol - d
Unit - Meters (m)
Magnetic flux
Symbol - Φ
Unit - Webers (Wb)
Magnetic field strength
Symbol - B
Unit - Teslas (T) or Weber per square meter (Wb m^-2)
Electromotive force (EMF)
Symbol - E
Unit - Volts (V)
Inductance
Symbol - L
Unit - Henrys (H)
Current
Symbol - I
Unit - Amps (A)
Time
Symbol - t
Unit - Seconds (s)
Mutual inductance
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
Alternating voltage
Symbol - Vp
Unit - Volts (V)
Number of turns on primary coil
Symbol - Np
Number of turns on secondary coil
Symbol - Ns
Voltage across secondary coil
Symbol - Vs
Units - Volts (V)
Angular frequency
Symbol - ω
Units - Radians per second (s^-1)
Power
Symbol - P
Units - Watts (W) or Joules per second (Js^-1)
Peak current
Symbol - Imax
Units - Amps (A)
Peak voltage
Symbol - Vmax
Units - Volts (V)
Root mean square current
Symbol - Irms
Units - Amps (A)
Root mean square voltage
Symbol - Vrms
Units - Volts (V)
Reactance of a capacitor
Symbol - Xc
Units - Ohms (Ω)
Reactance of an inductor
Symbol - Xl
Units - Ohms (Ω)
Impedance
Symbol - Z
Units - Ohms (Ω)
Frequency
Symbol - f
Units - Hertz (Hz)
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)
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).
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
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)
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)
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
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
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
Equation for efficiency of a transformer
Ef = VsIs / VpIp x 100
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).
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
Converting from mA to A
mA / 1000 = A
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
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
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
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)
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
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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
Voltage relationships at resonance
At resonance Xl = Xc,
thus Vl = Vc
At resonance Z = R
thus Vs = Vr = IR
