Basic ElectricityUnit 2

Basic Instrumentation

Outlines

• Terms related to basic electricity-Definitions of EMF, Current, Potential Difference, Power, Energy and Efficiency

• Definition: Resistance, resistivity & conductivity and their units

• Factors affecting resistance

• Ohm’s law

• Kirchhoff’s Laws of current & voltage

• Measurement of unknown resistance by Wheatstone bridge

• Terms related to A.C. (alternating current)

• Classification of electrical measuring instruments.

Terms related to basic electricity-Definitions of EMF, Current, Potential Difference, Power, Energy and Efficiency.

Electrical Voltage or Electro Motive Force (EMF)

• Electrical voltage is defined as electric potential difference between two points of an electric field.

• Using water pipe analogy, we can visualize the voltage as height difference that makes the water flow down.

V = φ2 - φ1

• V is the voltage between point 2 and 1 in volts (V).

• φ2 is the electric potential at point #2 in volts (V).

• φ1 is the electric potential at point #1 in volts (V).

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Electric current definition

• Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit.

• Using water pipe analogy, we can visualize the electrical current as water current that flows in a pipe. The electrical current is measured in ampere (amp) unit.

• Electrical current is measured by the rate of electric charge flow in an electrical circuit:

i(t) = dQ(t) / dt

• The momentary current is given by the derivative of the electric charge by time.

• i(t) is the momentary current I at time t in amps (A).

• Q(t) is the momentary electric charge in coulombs (C).

• t is the time in seconds (s).

Potential Difference

• The voltage difference between any two points in a circuit is known as the Potential Difference, pd or Voltage Drop and it is the difference between these two points that makes the current flow.

• The standard metric unit on electric potential difference is the volt, abbreviated V and named in honor of Alessandro Volta. One Volt is equivalent to one Joule per Coulomb. If the electric potential difference between two locations is 1 volt, then one Coulomb of charge will gain 1 joule of potential energy when moved between those two locations. If the electric potential difference.

Difference Between Electromotive Force (emf) and Potential Difference• Emf is the total voltage in the battery while the potential difference is

the work done in moving a charge against the electric field between two specific points in the circuit.

• Emf is always greater than the potential difference.

• The concept of emf is applicable only to an electrical field while the potential difference is applicable to magnetic, gravitational, and electric fields.

Power

• Power is the rate of doing work and is measured in Watt (W) or kilo-Watt (kW).

• Electrical power is defined as the rate at which electrical energy is supplied to a circuit or consumed by a load. The equation for calculating the power delivered to the circuit or consumed by a load was derived to be

P = ΔV • I

• To find the Power (P)

[ P = V x I ] P (watts) = V (volts) x I (amps)

• Also,

[ P = V2 ÷ R ] P (watts) = V2 (volts) ÷ R (Ω)

• Also,

[ P = I2 x R ] P (watts) = I2 (amps) x R (Ω)

Energy

• Energy is the total amount of work that is done and is measured in kilo-Watt-hour (kWh).

• Electrical Energy is the capacity to do work, and the unit of work or energy is the joule ( J ). Electrical energy is the product of power multiplied by the length of time it was consumed.

• In other words, Energy = power x time and Power = voltage x current. Therefore electrical power is related to energy and the unit given for electrical energy is the watt-seconds or joules.

Efficiency

• Power efficiency is defined as the ratio of the output power divided by the input power:

• η = 100% · Pout / Pin

• η is the efficiency in percent (%). Pin is the input power consumption in watts (W). Pout is the output power or actual work in watts (W).

Definition: Resistance, resistivity & conductivity and their units

Resistance

• Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it.

• Resistance is the property of material to oppose the flow of current through it.

R=(ρl)/a• Where,

• L = length in meters• A = cross sectional area in sq.meter• ρ = resistivity in ohm–meters• R = Resistance in ohms

• The resistance is measured in units of ohms (Ω).• If we make an analogy to water flow in pipes, the resistance is bigger when

the pipe is thinner, so the water flow is decreased.

Resistivity

• The electrical resistivity of a material is also known as its specific electrical resistance. It is a measure of how strongly a material opposes the flow of electric current.

• A definition of resistivity is the electrical resistance per unit length and per unit of cross-sectional area for a particular material at a specified temperature.

• The SI unit of electrical resistivity is the ohmmeter (Ωm). It is commonly represented by the Greek letter ρ, rho.

Conductivity

• Electrical conductivity or electrical conductance has a measure of how an electrical current moves within a substance. The higher the conductivity, the greater the current density for a given applied potential difference.

• The electrical conductivity or electrical conductance of a substance is a measure of its ability to conduct electricity.

• The electrical conductivity units are Siemens per meter, Sm^-1.

• The Siemens also used to be referred to as a mho - this is the reciprocal of an ohm, and this is inferred by spelling ohm backwards.

• Conductance is the reciprocal of resistance and one Siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho.

Factors affecting resistance

Factors affecting resistance

• Resistance is proportional to length

• Resistance is inversely proportional to cross-sectional-area

• Resistance depends on the material the wire

• Resistance increases with the temperature of the wire

𝐑 = 𝛒l

a

Resistance is proportional to length

• If you take a wire of different lengths and give each a particular potential difference across its ends, the longer the wire, the less volts each centimeter of it will get.

• This means that the 'electric slope' that makes the electrons move gets less steep as the wire gets longer, and the average drift velocity of electrons decreases.

• The correct term for this 'electric slope' is the potential gradient. A smaller potential gradient (less volts per meter) means current decreases with increased length and resistance increases.

𝐑 = 𝛒l

a

Resistance is inversely proportional to cross-sectional-area• The bigger the cross sectional area of the wire the

greater the number of electrons that experience the 'electric slope' from the potential difference.

• As the length of the wire does not change, each cm still gets the same number of volts across it - the potential gradient does not change and so the average drift velocity of individual electrons does not change.

• Although they do not move any faster there are more of them moving so the total charge movement in a given time is greater and current flow increases.

• This means resistance decreases. This does not give rise to a straight line graph as cross sectional area is inversely proportional to resistance not directly proportional to it.

𝐑 = 𝛒l

a

Resistance depends on the material the wire

• The more tightly an atom holds on to its outermost electrons, the harder it will be to make a current flow.

• The electronic configuration of an atom determines how willing the atom will be to allow an electron to leave and wander through the lattice.

• If a shell is almost full the atom is reluctant to let its electrons wander and the material it is in is an insulator.

• If the outermost shell (or sub-shell with transition metals) is less than half full then the atom is willing to let those electrons wander and the material is a conductor.

𝐑 = 𝛒l

a

Resistance increases with the temperature of the wire• The hotter wire has a larger resistance because of increased vibration

of the atomic lattice.

• When a material gets hotter the atoms in the lattice vibrate more.

• This makes it difficult for the electrons to move without interaction with an atom and increases resistance.

• The relationship between resistance and temperature is not a simple one.

𝑹𝒕 = 𝑹𝒐(𝟏 + 𝜶𝑻)

• Where Rt = resistance at temperature T, Ro is the resistance at 0 C , 𝛼(alpha) is the thermal resistance coefficient, T is temperature

Ohm’s law

Ohm’s law

• Georg Ohm found that, at a constant temperature, the electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and also inversely proportional to the resistance.

• This relationship between the Voltage, Current and Resistance forms the basis of Ohms Law and is shown below.

Ohm’s law

• By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohms Law to find the third missing value. Ohms Law is used extensively in electronics formulas and calculations so it is “very important to understand and accurately remember these formulas”.

• To find the Voltage, ( V )

[ V = I x R ] V (volts) = I (amps) x R (Ω)

• To find the Current, ( I )

[ I = V ÷ R ] I (amps) = V (volts) ÷ R (Ω)

• To find the Resistance, ( R )

[ R = V ÷ I ] R (Ω) = V (volts) ÷ I (amps)

Ohm’s law

• Ohms Law Example

• For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R) and the Power (P).

• Voltage [ V = I x R ] = 2 x 12Ω = 24V

• Current [ I = V ÷ R ] = 24 ÷ 12Ω = 2A

• Resistance [ R = V ÷ I ] = 24 ÷ 2 = 12 Ω

• Power [ P = V x I ] = 24 x 2 = 48W

Kirchhoff’s Laws of current & voltage

Kirchhoff's First Law – The Current Law, (KCL)

• Kirchhoff's Current Law or KCL, states that the “total current or charge entering a junction or node is exactly equal to the charge leaving the node as it has no other place to go except to leave, as no charge is lost within the node“.

• In other words the algebraic sum of ALL the currents entering and leaving a node must be equal to zero.

• I(exiting) + I(entering) = 0. This idea by Kirchhoff is commonly known as the Conservation of Charge.

Kirchhoff's First Law – The Current Law, (KCL)

• Here, the 3 currents entering the node, I1, I2, I3 are all positive in value and the 2 currents leaving the node, I4 and I5 are negative in value. Then this means we can also rewrite the equation as;

I1 + I2 + I3 – I4 – I5 = 0

• The term Node in an electrical circuit generally refers to a connection or junction of two or more current carrying paths or elements such as cables and components. We can use Kirchhoff's current law when analyzing parallel circuits.

Kirchhoff's Second Law – The Voltage Law, (KVL)• Kirchhoff's Voltage Law or KVL, states that “in any closed loop

network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is also equal to zero.

• In other words the algebraic sum of all voltages within the loop must be equal to zero.

• This idea by Kirchhoff is known as the Conservation of Energy.

Kirchhoff's Second Law – The Voltage Law, (KVL)• Starting at any point in the loop continue in

the same direction noting the direction of all the voltage drops, either positive or negative, and returning back to the same starting point.

• It is important to maintain the same direction either clockwise or anti-clockwise or the final voltage sum will not be equal to zero. We can use Kirchhoff's voltage law when analyzing series circuits.

Measurement of unknown resistance by Wheatstone bridge

Wheatstone bridge

• A Wheatstone bridge circuit has two input terminals and two output terminals consisting of four resistors configured in a diamond-like arrangement as shown. This is typical of how the Wheatstone bridge is drawn.

• The Wheatstone Bridge circuit is nothing more than two simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground producing zero voltage difference between the two parallel branches when balanced.

Wheatstone bridge

• We can see that the resistance ratio of these two parallel arms, ACB and ADB, results in a voltage difference between 0 volts (balanced) and the maximum supply voltage (unbalanced), and this is the basic principal of the Wheatstone Bridge Circuit.

• Balance occurs when:

Terms related to A.C. (alternating current)

Terms related to A.C. (alternating current)

Cycle:

• A complete positive and negative wave of an alternating current, after which signal repeats itself is known as cycle.

Frequency:

• The Frequency, (ƒ) is the number of times the waveform repeats itself within a one second time period.

• Frequency is the reciprocal of the time period, ( ƒ = 1/T ) with the unit of frequency being the Hertz, (Hz).

Time period:

• The Period, (T) is the length of time in seconds that the waveform takes to repeat itself from start to finish.

• This can also be called the Periodic Time of the waveform for sine waves, or the Pulse Width for square waves.

Terms related to A.C. (alternating current)

Amplitude:

• The Amplitude (A) is the magnitude or intensity of the signal waveform measured in volts or amps.

Average:

• The average or mean value of a continuous DC voltage will always be equal to its maximum peak value as a DC voltage is constant. This average value will only change if the duty cycle of the DC voltage changes.

• In a pure sine wave if the average value is calculated over the full cycle, the average value would be equal to zero as the positive and negative halves will cancel each other out. So the average or mean value of an AC waveform is calculated or measured over a half cycle only and this is shown below.

For a pure sinusoidal waveform this average or mean value will always be equal to 0.637 x Vmax and this relationship also holds true for average values of current.

Terms related to A.C. (alternating current)

RMS value: • The effective current in an AC system is called the Root Mean Squared or

R.M.S. value and RMS values are the DC equivalent values that provide the same power to the load.

• The effective or RMS value of an alternating current is measured in terms of the direct current value that produces the same heating effect in the same value resistance. The RMS value for any AC waveform can be found from the following modified average value formula.

• For a pure sinusoidal waveform this effective or R.M.S. value will always be equal to 1/√2 x Vmax which is equal to 0.707 x Vmax and this relationship holds true for RMS values of current.

Terms related to A.C. (alternating current)

• AC Waveform Example

1. What will be the periodic time of a 50Hz waveform?

2. What is the frequency of an AC waveform that has a periodic time of 10mS.

Classification of electrical measuring instruments.

Classification of electrical measuring instruments• They are classified as

• Indicating Instruments: These instruments provide information regarding the variable quantity under measurement and most of the time this information are provided by the deflection of the pointer. This kind of function is known as the indicating function of the instruments. PMMC, MI, dynamometer wattmeter, frequency meter, power factor meter are examples.

• Recording Instruments: These instruments usually use the paper in order to record the output. This type of function is known as the recording function of the instruments. Examples are recording voltmeter, recording wattmeter, storage oscilloscope.

• Integrating Instruments: This type of instruments are used to measure total units with respect to time. It does not shows current measurement but gives total of that quantity. For Example energy meter, Mass flow meter.

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