Magnetism and Electromagnetism

Chapter 39: Magnetism and Electromagnetism

• Reviews magnetic flux, flux density, force on current-carrying conductors, and force on a charge

Magnetic Flux and Flux Density

• Flux is equal to 150 × 10-6 Wb in a magnetic pole face.
• A cross-sectional area A is equal to 20,000 × 10-6 m2
• The relationship leads to a flux density B = 0.0075 T or 7.5 mT

Force on a Current-Carrying Conductor

• Studies a conductor carrying a current 20 A at right angles to a 0.9 T magnetic field
• The conductor is 30 cm (0.30m) inside the field
• The force acting on the conductor is 5.4 N
• When inclined at a 30° angle to the field, the force becomes 2.7 N

Force on a Charge

• An electron has a charge of 1.6 × 10-19 coulombs.
• Travels at 3 × 107 m/s perpendicular to a 18.5 μT field.
• The force exerted on the electron in the field is 8.88 × 10–17 N

Magnetic Field Between Circular Pole Faces

• A conductor of 350mm (0.35m) length carries a current of 10 A at right angles to a magnetic field
• The field is between two circular pole faces each of 60mm radius.
• If a total flux between the pole faces is 0.5mWb (0.5 x 10-3 Wb)
• The magnitude of the force exerted on the conductor is calculated as 0.155 N

Chapter 40: Electromagnetic Induction

• Examines the laws of electromagnetic induction, mutual inductance, and transformers

Laws of Electromagnetic Induction

• M is the mutual inductance between two coils, and is measured in henries
• dl1/dt is the rate of change of current in the first coil

Current Flow in a Conductor Moving in a Magnetic Field

• A conductor 300mm long moves at a uniform speed of 4 m/s at right-angles to a uniform magnetic field of 1.25 T
• The induced e.m.f. E = 1.5 V
• If the conductor ends are open-circuited, no current flows, this is despite the 1.5V induced
• If ends are connected to a 20 Ω load, the current is 0.075 A or 75mA, using Ohm's law

Magnitude of Induced EMF from a Conductor

• A conductor moves at 15 m/s at varying angles to a magnetic field
• There are two square-faced poles of side length 2 cm.
• The flux leaving the pole face is 5 μWb.
• Results depend on the angle:
  • The magnitude of the induced e.m.f. at 90° is 3.75 mV
  • The magnitude of the induced e.m.f. at 60° is 3.25 mV
  • The magnitude of the induced e.m.f. at 30° is 1.875 mV

Mutual Inductance Calculations

• The mutual inductance in henries between two coils is calculated as 0.0075 H or 7.5mH
• Here, a current changing at 200 A/s in one coil induces an e.m.f. of 1.5 V in another,

Calculating Rate of Change of Current

• Mutual inductance between two coils is 18 mH
• To induce an e.m.f. of 0.72 V in the other, the steady rate of change of current in one coil is 40 A/s

Ideal Transformer Ratio, Voltage and Current:

• An ideal transformer has a turns ratio of 8:1
• With a primary current of 3 A at 240 V, the secondary voltage is 30 volts and current is 24 A

Determining Current and Turns Ratio

• An ideal transformer connected to 240 V mains supplies a 12 V, 150 W lamp
• The transformer turns ratio is calculated as 20 and a current taken from the supply being 0.625 A

Chapter 41: Alternating Voltages and Currents

Waveforms

• Focuses on waveform shapes and measurements related to alternating current

Frequency and Periodic Time

• Frequency f = 1 or f = 1 T T

Frequency Calculation from Periodic Time

• For a periodic time of 4 ms, the frequency is 250 Hz
• For a periodic time of 8 μs, the frequency is 125 kHz or 0.125 MHz

Frequency Calculation from Number of Cycles

• Alternating current completes 5 cycles in 8 ms
• The frequency is 625 Hz

A.C Values

Periodic Waveforms

• This is useful for calculating frequency, average value, RMS value, form factor and peak factor

RMS Value Calculation- Sinusoidal Current

• The root mean square of a sinusoidal current of maximum value 20 A is 14.14 A

Maximum Value and RMS

• For a supply voltage having a mean value of 150 V, and assuming it to be a sine wave, the maximum value is 235.5 V
• The RMS value is 166.5 V

Peak and Mean Value

• For a 240V mains supply (RMS), the Peak value is 339.V
• The Mean value is 216.3 V

Chapter 42: Capacitors and Inductors

Capacitors

Capacitors and Capacitance

• The absolute permittivity equation is reviewed

Potential Difference Between Plates

• A 4 A direct current flows into a 20 μF capacitor for 3 ms
• A potential difference between the plates is 600 V

Flux Density Strength

• Two parallel 20 cm by 40 cm plates carry a charge of 0.2 μC
• A calculation of the electric flux density gives 2.5 μC/m^2
• The plates are spaced 5 mm apart, the voltage between them being 0.25 kV.
• The electric field strength can be calculated as 50 kV/m

Calculating Capacitance

• For n parallel connected capacitors, the capacitance is; C = C1 + C2 + C3... + Cn
• For n series connected capacitors, the inverse of the capacitance is; 1 / C = // C1 + 1 / C2 + 1 / C3... + 1 / Cn

Ceramic Capacitor

• A ceramic capacitor has a 4 cm^2 plate area with 0.1mm ceramic separation, and a relative permittivity of 100
• The calculation of the capacitance gives you 3540 pF
• Giving capacitor 1.2 μC gives a potential difference 339 V

Parallel Plate Capacitor

• 19 inter-leaved plates, (75 mm^2) and separated by 0.2 mm mica sheets
• Relative permittivity of the mica is 5
• The capacitance is 0.0224 μF or 22.4 nF

Equivalent Capacitance when Connected in Parallel

• Capacitors of 6μF and 4μF in parallel has a capacitance of 10μF
• Capacitors of 6μF and 4μF in series has a capacitance of 2.4 μF

Series Connection of Capacitors

• Examines applying a 350V supply across series connections of capacitances of 3, 6 and 12 μF
• Equivalent circuit capacitance, can be found to be 1.714 μF
• Total charge calculates to 0.6mC, which because of series connection, applies to all
• Voltages can be found for each, with 200V across the 3μF, 100V across the 6μF and 50V across the 12μF

The Capacitor, Dielectric Strength, Thickness

• The capacitor has to be constructed with 0.2μF
• It must be able to withstand 1.25kV across the terminals
• Mica is used as the dielectric providing 50MV/m
• Thickness can be found to be 0.025mm
• With a relative permittivity of 6, plate can have area 941.6cm^2

Stored Energy

• Explains energy stored by capacitor, which calculates to ½CV^2
• This also introduces the formulas for power such as energy / time = watts

Energy Stored in a Capacitor

• A 3μF capacitor is charged to 400 V
• The energy stored is 0.24 J
• If dissipated in 10 μs, the average power developed is 24 kW

Potential Difference of a capacitor at 4 Joules of Energy.

• 12μF
• PD is 816.5V

Inductance

• Explains inductance parameters, like induced electromotive force in turns, coils and inductance
• Energy stored by inductors and inductance of a coil are also assessed

Induced Electromotive Force

• The calculated e.m.f induced can be found to be -100V
• Based on a flux change of 25 mWb in a coil that consists of 200 turns with change occurring in 50 ms

E.M.F and Inductance

• The calculated e.m.f induced, can be found to be -48 volts
• An inductance 12H contains a current with changing rate of 4 A / s

Changing Current

• 1.5 kV e.m.f with inductance is shown, when current of 4 A drops to 0 over the period of 8ms.
• The inductance of the circuit is 3H

Magnetic Field

• 8H inductor is measured, this has a current of 3 A passing through
• In the inductors magnetic field, 36 joules of energy is stored

A Coil

• Current of 4A passes through a coil of 800 turns This makes 5 mWb of flux
• The inductance is 1 H

Stored Energy and Calculating Average EMF.

• 3A of current passes through a coil with 1500 turns This has linking flux of 25 mWb
• The Inductance of the coil is 12.5H
• 56.25J is the energy the a has to store
• The Average EMF is -250V, but decreases to 0 across 150 ms

Chapter 43: Electrical Measuring Instruments and Measurements

• Presents principles and equations related to measurement errors and instrumentation loading

Instrumentation and Loading

• The operating of various instruments, is dependent to the circuit and measured power
• Fundamental circuits might change with loading effect
• Resistance may be found using volts, often stated as 'kΩ/volt'
• Ideally Voltmeters have a high resistance

Voltmeter Installation

When resistance = 250Ω , a voltmeter will dissipate 5mW of power, however 40 W is still dissipated. Compared to watts lost, voltmeter is an insignificant difference And uses 10k Ω/V

Ammeter Loading

• Ammeter, with f.s.d. of 100mA and resistance of 50Ω connects, when voltage is 10V and a load is present at 500 Ω,.
• Ammeter makes alterations within a circuit through, through its resistance through, 20 mA - 18.18MA
• However the power doesn't change majorly, as it gets to 16.53 MW
• Due, the power dissipation is 165.3 MW

Oscilloscope Utilization

• Oscilloscope is utilized to graph displaying signals is that are electronic
• Graphs shows signals over specific period It can assess Time and Values + wave form +frequency of signal To establish voltage or DC and to reduce Noise

Utilization of Oscilloscopes

• Analyzing DC with "volts/cm" switch
• Analyzing AC with "time/cm", is at a certain frequency

Calculation of the Pulse.

• Calculation, that uses "time/cm" switch, where 50ms/cm and voles/cm switch is 0.2V/CM Periodic Time is- 175ms
• Wave length is 5.71 Hx
• Magnitude, is . 68V

Double Beam

• .01 and 2V, in a double wave oscilloscope with , 100 s/cm switch for "times"
• The 2KHz is the waveforms frequencies
• A Waveform Is 28.3V
• In phase with each 78

Waveform

• Represents the cycle
• In between the 36
• Wave shows, which gets lead

Wheatstone Bridge

Explains the bridge and balance between R1, R2, R3, Rx

Calculation.

Wheatstone 400 Is in 4K @ R This happens, during a balance.

D.C Potentiometer

• Is based on balance
• Reference figure, on a value