1
Q
Conduction in Metals
A
- Electric Charge is the most basic quantity in an electric circuit.
- Charge, ‘e’, on an electron is negative and equal in magnitude to 1.602x10^-19 C.
- The coulomb is a large unit for charges.
- In 1C of charge there are (1/1.602x10^-19)=6.24x10^18 electrons.
- Realistic lab values of charges are in the order of μC(-6), nC(-9) or pC(-12).
2
Q
How do charges move?
A
- Motion of charges creates electric current.
- Charges flow in drift direction.
- The law of conservation of charges states that charges can neither be created nor destroyed, only transferred.
- Sum of charges in a system does not change.
- Total energy gained per unit charge = Total energy lost per unit charge.
- This is because both energy and charge are conserved.
- Charge is created and injected into the negative terminal of the source and the same amount of charge is neutralized at the positive side of the source thus creating a current flow in the body.
- In an atom, each orbiting electron is at a certain energy level.
- In order for an electron to move from its orbit, it must be acted upon by some force.
- In insulators, the orbiting electrons are held tightly by the attracting force of the nucleus and within the atomic matrix.
- In conductors, however, the outer electrons respond to stimuli and can leave their orbit.
- Stimulus examples:
- Heat, random emission of electrons.
- EMF, unidirectional emissions of electrons ( battery, generator).
- Stimulus examples:
3
Q
Voltage and Current
A
- EMF is able to impart energy to outer electrons.
- Unit of EMF is volt (V)- it is the measure of the amount of energy transferred to the electron.
- Current )A) is the measure of the amount of charge flow in unit time.
i = dq/dt (q is charge in coulombs, t is time in seconds)
1A = 1C/s - The voltage Vab between 2 points a and b in an electric circuit is the enrgy(work done) needed to move 1C of charge from a to b.
Vab = dw/dq (w is energy in joules)
1V = 1J/C = 1Nm/C
4
Q
Power and Energy
A
- Power is the time rate of expending or absorbing energy, measured in watts (W).
p = dw/dt = dw/dq x dq/dt = vi - Energy is the capacity to do work, measured in joules (J)
Electrical energy = Power(watts) x time(seconds)
= VIt(joules)
5
Q
Resistivity
A
- A measure of a material’s ability to oppose the flow of an electric current.
- It depends on the type of material and its temperature
- Gold and silver are used for high quality contacts in computers and instruments.
6
Q
Resistance
A
- It is directly proportional to its length and inversely proportional to its cross-sectional area, measured in ohms (Ω).
Resistance, R = (Resistivity x Length)/Area
R = ρL/A - The reciprocal of resistance (R) is called conductance (G) and is measured in siemens (S).
- 1Ω is defined as a constant potential of 1V applied between 2 points produces a current flow of 1A.
R = V/I
1Ω = 1V/A
7
Q
Ohm’s Law
A
-The voltage (V) across a resistor is directly proportional to the current (I) flowing through the resistor, provided that its temperature remains constant.
V α I
V = I x R
R = V/ I
8
Q
Equivalent Resistance
A
- Open circuit
- Infinite resistance (insulator)
- Zero current flow
- Short circuit
- Zero resistance (conductor)
- Infinite current flow
9
Q
Temperature Effects
A
- When temp increases:
- No. of free electrons/unit volume in the metal is unchanged.
- The metal atoms in crystal lattice vibrate w/ greater amplitude.
- No. of collisions between the free electrons and metal atoms increase.
- Electron flow slows down and therefore the resistance of the metal increases.
- vice versa
10
Q
Temperature Coefficient of Resistance
A
- It measures how much the resistance of a conductor increases with increase in temp.
R1 = R0 (1 + α0 θ1)
R - resistance at θ0
R1 - resistance at θ1C
R0 - resistance at 0 C (C is degrees C)
α0 - Temp coefficient of resistance at 0 C - Reason for keeping electrical equipment cool.
11
Q
Conventions
A
- Common letters signifies time varying values - i, v, p
- Capital letters signifies average or constant values - I, V, P, Q, S
- Current is the flow of electrons from negative to positive terminals.
- Conventional current flow is from positive to negative.
- Current leaves active components and thus they supply power.
- Current enters passive components (resistor) and thus they absorb electrical power. They don’t supply power.
12
Q
Electrical Symbols
A
- Active Elements
- Independent Voltage source
- Independent Current source
- D.C. Sources - Supply, Cell, Battery of cells, Current source.
- A.C. Sources - Voltage supply
- Passive Elements
- These don’t initially possess any stored electrical energy.
- Fixed value resistor (IEC symbol and IEEE symbol)
- Variable resistor (Potentiometer and Rheostat)
- Resistor, Load, Unpolarized Capacitor, Polarized Capacitor, Inductor (air core and Iron core)
- Filament Lamp, Fuse, Transformer, Motor
- Connections and measuring devices
- Connecting lead
- Junction of conductors
- Crossing conductors (not connected)
- Switch
- Earth
- Voltmeter
- Ammeter
- Ohmmeter
13
Q
Circuit Connections
A
- A node is the point of connection between 2 or more branches.
- Represented by a dot
- A branch reps any element(s) between 2 nodes.
- A loop is any closed path in a circuit (multiple branches)
14
Q
Kirchoff’s Current Law
A
- KCL is based on conservation of charge.
- KCL states that the algebraic sum of currents entering a node or a closed boundary is equal to zero.
sum of currents in system = 0
Current In = I1, I2, I3 (A current entering the node is positive)
Current Out = I4, I5 ( A current leaving the node is negative)
I1 + I2 + I3 + (-I4) + (-I5) = 0
I1 + I2 + I3 = I4 + I5 - Hence, the sum of currents entering a node is equal to the sum of currents leaving the same node.
15
Q
Kirchoff’s Voltage Law
A
- KVL is based conservation of energy.
- KVL states that the algebraic sum of all voltages around a closed path (a loop) is equal to zero.
sum of voltages in circuit = 0
V1 + (-V2) + (-V3) + (-V4) + (-V5) = 0
V1 = V2 + V3 + V4 + V5 - Hence, in a loop, the sum of voltages in one direction is equal to the sum of voltage in the opposite direction.
- A voltage source direction is defined.
- A voltage drop direction ( across a passive element) is opposite to that of the current flow (loop direction).
16
Q
Equivalent Resistance
A
- Series connection - when any 2 elements share the same node on 1 side of each element
V = V1 + V2 +V3 +…+ Vn
V = IR1 + IR2 + IR3 +…+ IRn = I (R1 + R2 + R3 +…+ Rn)
V/I = R1 + R2 + R3 +…+ Rn
Therefore,
Req = R1 + R2 +R3+..+ Rn - Parallel connection - when any 2 or more elements share the same nodes on either side of each element.
I = I1 +I2 + I3 +…+ In
I = V/R1 + V/R2 + V/R3 +…+ V/Rn =V(1/R1 + 1/R2 + 1/R3 +…+ 1/Rn)
I/V = (1/R1 + 1/R2 + 1/R3 +…+ 1/Rn)
Therefore,
1/Req= 1/R1 + 1/R2 + 1/R3 +…+ 1/Rn
17
Q
Voltage Divider Rule
A
- The voltage across a resistor within a loop is a fraction of the source voltage.
- This fraction is the resistance of that resistor over the total resistance in the loop.VR1 = E[R1/(R1 + R2)]
VR2 = E[R2/(R1 + R2)]
18
Q
Current Divider Rule
A
- The current through a resistor in a parallel branch is a fraction of the total current from the source.
- This fraction is the equivalent resistance of the resistor(s) in the other branch(es) over the total resistances in the circuit.
- It must be reduces to 2 branches before analysis.
Ix = It[ Rt/ (Rx + Rt)] - Rt is resolved in parallel.
ECNG 1007 Electrical Engineering Technology
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