Contents
1. VOLTAGE/CURRENT/ENERGY/POWER/EFFICIENCY ..................................................... 3
2. RESISTANCE ................................................................................................................................ 5
Questions: ......................................................................................................................................... 7
3. RESISTORS COMBINATIONS................................................................................................... 9
RESISTORS IN SERIES ............................................................................................................................. 9
RESISTORS IN PARALLEL ..................................................................................................................... 12
NETWORKS OF SERIES AND PARALLEL RESISTORS ............................................................................... 16
Questions: ....................................................................................................................................... 18
4. KIRCHOFF’S LAWS .................................................................................................................. 20
Questions ........................................................................................................................................ 26
5. CIRCUIT THEOREMS ............................................................................................................... 28
THEVENIN’S THEOREM........................................................................................................................ 28
SUPERPOSITION THEOREM ................................................................................................................... 31
Questions ........................................................................................................................................ 33
6. CAPACITORS .............................................................................................................................. 35
CAPACITORS IN SERIES ........................................................................................................................ 37
CAPACITORS IN PARALLEL .................................................................................................................. 39
ENERGY STORED ................................................................................................................................. 39
Questions ........................................................................................................................................ 40
7. MAGNETISM AND INDUCTANCE ......................................................................................... 41
ELECTROMAGNETISM .......................................................................................................................... 41
SOLENOID............................................................................................................................................ 41
FORCE ON A CURRENT CARRYING CONDUCTOR ................................................................................... 42
FARADAY’S LAW OF INDUCTION ......................................................................................................... 43
8. INDUCTANCE AND INDUCTORS........................................................................................... 44
9. TIME CONSTANTS .................................................................................................................... 46
Questions ........................................................................................................................................ 48
10. AC THEORY ............................................................................................................................ 49
11. WAVEFORM SHAPE ............................................................................................................. 50
12. PHASE DIFFERENCE ............................................................................................................ 52
13. POWER DISSIPATION IN AN AC CIRCUIT AND RMS VALUES................................. 55
14. COMPONENT BEHAVIOUR IN AC CIRCUITS ................................................................ 56
RESISTANCE. ....................................................................................................................................... 56
CAPACITANCE ..................................................................................................................................... 58
INDUCTANCE ....................................................................................................................................... 60
POWER ................................................................................................................................................ 61
15. SERIES RC AND RL CIRCUITS........................................................................................... 61
SERIES RC CIRCUIT ............................................................................................................................. 61
SERIES RL CIRCUIT ............................................................................................................................. 64
RLC CIRCUITS ..................................................................................................................................... 67
16. POWER FACTOR ................................................................................................................... 73
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 1
Sept 2017. Rev 1.6
,17. RESONANCE ........................................................................................................................... 78
Questions: ....................................................................................................................................... 81
18. RECTIFIERS AND REGULATORS ..................................................................................... 83
HALF WAVE RECTIFIER. ....................................................................................................................... 83
FULL WAVE RECTIFIER. ....................................................................................................................... 85
RECTIFIER WITH A CAPACITOR LOAD. .................................................................................................. 86
REGULATOR ........................................................................................................................................ 88
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 2
Sept 2017. Rev 1.6
,1. Voltage/Current/Energy/Power/Efficiency
The diagram above is a schematic for the battery circuit. Note that all corners are drawn at
right angles. The paths that connect elements ( battery and bulb ) are assumed to be ideal.
An electrical supply has two terminals – a positive and a negative. If an external
connection is made between the terminals ( i.e. if the supply is connected to a circuit )
then an electric current will flow.
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 3
Sept 2017. Rev 1.6
, The supply will push electric charge through the path between the terminals in a loop (
i.e. out of one terminal through the circuit and back in the other terminal ).
The measure of the ability of the supply to cause current to flow is the potential
difference between the terminals. The unit of potential difference is the Volt , V. The
terms potential difference and voltage are used interchangeably.
Typical values are 12V for a car battery , 220V for the mains supply in Europe , 110V for
the mains supply in the USA , 50V on a telephone line , 0-30V for a supply used in a lab
for experiments. The voltage rating alone does not indicate how powerful or dangerous
the electrical supply is. Any voltage above 50V is potentially lethal but only if the supply
can maintain it under the conditions of use. Static electricity can reach voltages of from
10kV to 100kV but is not dangerous to a person.
Voltage is a difference measurement. It’s formal definition is that it is a measure of the
work that needs to be done to move electric charge between two points. In order to make
it easier to make measurements in a circuit, it is necessary to define a common reference
point to which all voltage differences are compared. This point is traditionally called the
earth point or ground point and is given a numerical value of 0V. So if the voltage at a
point in a circuit is said to be 5V, then it is 5V higher than ground.
If an external circuit is connected to a voltage source then the effect is to cause current to
flow through the circuit. The supply pushes electrons out the negative terminal , through
the external circuit and back to the positive terminal ( but conventional current is said to
flow the other way). A circular path is set up. The amount of electrons the supply can
push through the circuit is dependent on what the external circuit is made of. Some
materials ( conductors ) will easily carry a large current for a small potential difference
(i.e. the supply only has to do a small amount of work to cause a large amount of charge
to move around the external circuit ) while other materials ( insulators ) will carry only a
small current for even a large potential difference ( i.e. the supply has to do a large
amount of work to cause even a small amount of charge to move around the external
circuit ).
The rate at which electrons move through the circuit is called the current. The unit of
current is the Ampere ( Amp ) , A. It is the rate of flow of charge per unit time –
Current = Charge/Time. ( I=Q/t ).
If a supply is pushing electrons around a circuit then it is expending energy / doing work /
dissipating power. It has an internal energy source ( e.g. a chemical imbalance in a battery
) that causes electrons to flow. The energy of this source is being used as the electrons are
pushed around the circuit. The unit of work is the Joule , J. It is also the unit of energy -
since energy is the ability to do work. The rate of doing work is power. The unit of power
is the Watt , W. One Watt equals one Joule per second.
The power that comes from the battery and pushes the charge through the circuit gets
transformed in the external circuit. If the load is a bulb then enough heat is generated to
cause the load to get so hot that it glows. If the load is an electric cooker then enough heat
is generated to allow food to be cooked. If the load is a motor then the electrical energy is
transformed into mechanical energy.
For measuring the energy consumption of domestic or business premises the Joule is too
small a unit. A more suitable unit for billing for use of electrical energy is the kilowatt-
hour ( kWh ). 1 kWh is the total energy used in 1 hour at a rate of 1kW ( i.e. 1000 J/sec
). [ 1 kWh = 1000 W * 3600 secs = 3.6MJ ].
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 4
Sept 2017. Rev 1.6
1. VOLTAGE/CURRENT/ENERGY/POWER/EFFICIENCY ..................................................... 3
2. RESISTANCE ................................................................................................................................ 5
Questions: ......................................................................................................................................... 7
3. RESISTORS COMBINATIONS................................................................................................... 9
RESISTORS IN SERIES ............................................................................................................................. 9
RESISTORS IN PARALLEL ..................................................................................................................... 12
NETWORKS OF SERIES AND PARALLEL RESISTORS ............................................................................... 16
Questions: ....................................................................................................................................... 18
4. KIRCHOFF’S LAWS .................................................................................................................. 20
Questions ........................................................................................................................................ 26
5. CIRCUIT THEOREMS ............................................................................................................... 28
THEVENIN’S THEOREM........................................................................................................................ 28
SUPERPOSITION THEOREM ................................................................................................................... 31
Questions ........................................................................................................................................ 33
6. CAPACITORS .............................................................................................................................. 35
CAPACITORS IN SERIES ........................................................................................................................ 37
CAPACITORS IN PARALLEL .................................................................................................................. 39
ENERGY STORED ................................................................................................................................. 39
Questions ........................................................................................................................................ 40
7. MAGNETISM AND INDUCTANCE ......................................................................................... 41
ELECTROMAGNETISM .......................................................................................................................... 41
SOLENOID............................................................................................................................................ 41
FORCE ON A CURRENT CARRYING CONDUCTOR ................................................................................... 42
FARADAY’S LAW OF INDUCTION ......................................................................................................... 43
8. INDUCTANCE AND INDUCTORS........................................................................................... 44
9. TIME CONSTANTS .................................................................................................................... 46
Questions ........................................................................................................................................ 48
10. AC THEORY ............................................................................................................................ 49
11. WAVEFORM SHAPE ............................................................................................................. 50
12. PHASE DIFFERENCE ............................................................................................................ 52
13. POWER DISSIPATION IN AN AC CIRCUIT AND RMS VALUES................................. 55
14. COMPONENT BEHAVIOUR IN AC CIRCUITS ................................................................ 56
RESISTANCE. ....................................................................................................................................... 56
CAPACITANCE ..................................................................................................................................... 58
INDUCTANCE ....................................................................................................................................... 60
POWER ................................................................................................................................................ 61
15. SERIES RC AND RL CIRCUITS........................................................................................... 61
SERIES RC CIRCUIT ............................................................................................................................. 61
SERIES RL CIRCUIT ............................................................................................................................. 64
RLC CIRCUITS ..................................................................................................................................... 67
16. POWER FACTOR ................................................................................................................... 73
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 1
Sept 2017. Rev 1.6
,17. RESONANCE ........................................................................................................................... 78
Questions: ....................................................................................................................................... 81
18. RECTIFIERS AND REGULATORS ..................................................................................... 83
HALF WAVE RECTIFIER. ....................................................................................................................... 83
FULL WAVE RECTIFIER. ....................................................................................................................... 85
RECTIFIER WITH A CAPACITOR LOAD. .................................................................................................. 86
REGULATOR ........................................................................................................................................ 88
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 2
Sept 2017. Rev 1.6
,1. Voltage/Current/Energy/Power/Efficiency
The diagram above is a schematic for the battery circuit. Note that all corners are drawn at
right angles. The paths that connect elements ( battery and bulb ) are assumed to be ideal.
An electrical supply has two terminals – a positive and a negative. If an external
connection is made between the terminals ( i.e. if the supply is connected to a circuit )
then an electric current will flow.
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 3
Sept 2017. Rev 1.6
, The supply will push electric charge through the path between the terminals in a loop (
i.e. out of one terminal through the circuit and back in the other terminal ).
The measure of the ability of the supply to cause current to flow is the potential
difference between the terminals. The unit of potential difference is the Volt , V. The
terms potential difference and voltage are used interchangeably.
Typical values are 12V for a car battery , 220V for the mains supply in Europe , 110V for
the mains supply in the USA , 50V on a telephone line , 0-30V for a supply used in a lab
for experiments. The voltage rating alone does not indicate how powerful or dangerous
the electrical supply is. Any voltage above 50V is potentially lethal but only if the supply
can maintain it under the conditions of use. Static electricity can reach voltages of from
10kV to 100kV but is not dangerous to a person.
Voltage is a difference measurement. It’s formal definition is that it is a measure of the
work that needs to be done to move electric charge between two points. In order to make
it easier to make measurements in a circuit, it is necessary to define a common reference
point to which all voltage differences are compared. This point is traditionally called the
earth point or ground point and is given a numerical value of 0V. So if the voltage at a
point in a circuit is said to be 5V, then it is 5V higher than ground.
If an external circuit is connected to a voltage source then the effect is to cause current to
flow through the circuit. The supply pushes electrons out the negative terminal , through
the external circuit and back to the positive terminal ( but conventional current is said to
flow the other way). A circular path is set up. The amount of electrons the supply can
push through the circuit is dependent on what the external circuit is made of. Some
materials ( conductors ) will easily carry a large current for a small potential difference
(i.e. the supply only has to do a small amount of work to cause a large amount of charge
to move around the external circuit ) while other materials ( insulators ) will carry only a
small current for even a large potential difference ( i.e. the supply has to do a large
amount of work to cause even a small amount of charge to move around the external
circuit ).
The rate at which electrons move through the circuit is called the current. The unit of
current is the Ampere ( Amp ) , A. It is the rate of flow of charge per unit time –
Current = Charge/Time. ( I=Q/t ).
If a supply is pushing electrons around a circuit then it is expending energy / doing work /
dissipating power. It has an internal energy source ( e.g. a chemical imbalance in a battery
) that causes electrons to flow. The energy of this source is being used as the electrons are
pushed around the circuit. The unit of work is the Joule , J. It is also the unit of energy -
since energy is the ability to do work. The rate of doing work is power. The unit of power
is the Watt , W. One Watt equals one Joule per second.
The power that comes from the battery and pushes the charge through the circuit gets
transformed in the external circuit. If the load is a bulb then enough heat is generated to
cause the load to get so hot that it glows. If the load is an electric cooker then enough heat
is generated to allow food to be cooked. If the load is a motor then the electrical energy is
transformed into mechanical energy.
For measuring the energy consumption of domestic or business premises the Joule is too
small a unit. A more suitable unit for billing for use of electrical energy is the kilowatt-
hour ( kWh ). 1 kWh is the total energy used in 1 hour at a rate of 1kW ( i.e. 1000 J/sec
). [ 1 kWh = 1000 W * 3600 secs = 3.6MJ ].
Paddy Collins MECH7004 : Electrical Engineering I for Mech Eng Page 4
Sept 2017. Rev 1.6
