Some Useful Laws in Basic Electronics

Kirchhoff’s laws state

Current Law At any junction in an electric circuit the total current flowing towards that junction is equal to the total current flowing away from the junction

 

(b) Voltage Law

In any closed loop in a network, the algebraic sum of the voltage drops (i.e. products of current and resistance) taken around the loop is equal to the resultant e.m.f. acting in that loop Thus, referring to Figure  E1 - E2 = IR1 + IR2 +IR3

The superposition theorem

In any network made up of linear resistances and containing more than one source of e.m.f., the resultant current flowing in any branch is the algebraic sum of the currents that would flow in that branch if each source was considered separately, all other sources being replaced at that time by their respective internal resistances

 

Power and Power Factor in an AC Circuit

Power consumed by a resistor is dissipated in heat and not
returned to the source. This is true power. True power is the rate
at which energy is used.
Current in an AC circuit rises to peak values and diminishes to
zero many times a second. The energy stored in the magnetic
field of an inductor, or plates of a capacitor, is returned to the
source when current changes direction.
Although reactive components do not consume energy, they do
increase the amount of energy that must be generated to do
the same amount of work. The rate at which this non-working
energy must be generated is called reactive power.
Power in an AC circuit is the vector sum of true power and
reactive power. This is called apparent power. True power is
equal to apparent power in a purely resistive circuit because
voltage and current are in phase. voltage and current are also in
phase in a circuit containing equal values of inductive reactance
and capacitive reactance. If voltage and current are 90 degrees
out of phase, as would be in a purely capacitive or purely
inductive circuit, the average value of true power is equal to
zero. There are high positive and negative peak values of power,
but when added together the result is zero

True Power and  Apparent Power Formulas The formula for apparent power is  P = EI

Apparent power is measured in volt-amps (VA). True power is calculated from another trigonometric function  the cosine of the phase angle (cos θ). The formula for true power is

P = EI  cos  θ

True power is measured in watts  In a purely resistive circuit, current and voltage are in phase There is a zero degree angle displacement between current and voltage. The cosine of zero is one. Multiplying a value by one does not change the value. In a purely resistive circuit the cosine of the angle is ignored. In a purely reactive circuit, either inductive or capacitive, current and voltage are 90 degrees out of phase. The cosine of 90 degrees is zero. Multiplying a value times zero results in a zero product. No power is consumed in a purely reactive circuit

Calculating Apparent Power in a simple R-L-C Circuit In the following 120 volt circuit, current is equal to 84.9 milliamps. Inductive reactance is 100 Ω and capacitive reactance is 1100 Ω. The phase angle is -45 degrees. By referring to a trigonometric table, the cosine of -45 degrees is found to be .7071.

 

 

The apparent power consumed by the circuit is:

P = EI
P = 120 x 0.0849
P = 10.2 VA
The true power consumed by the circuit is:
P = EI cos θ
P = 120 x 0.0849 x 0.7071
P = 7.2 Watts
Another formula for true power is:
P = I2R
P = 0.08492 x 1000
P = 7.2 Watts

Power Factor

Power factor is the ratio of true power to apparent power in an
AC circuit. Power factor is expressed in the following formula

PF= True Power / Apparent Power

Power factor can also be expressed using the formulas for true
power and apparent power. The value of EI cancels out because
it is the same in the numerator and denominator. Power factor
is the cosine of the angle PF = EI cos θ / EI =  cos θ

In a purely resistive circuit, where current and voltage are in
phase, there is no angle of displacement between current and
voltage. The cosine of a zero degree angle is one. The power
factor is one. This means that all energy delivered by the source
is consumed by the circuit and dissipated in the form of heat.
In a purely reactive circuit, voltage and current are 90 degrees
apart. The cosine of a 90 degree angle is zero. The power factor
is zero. This means the circuit returns all energy it receives from
the source to the source.
In a circuit where reactance and resistance are equal, voltage
and current are displaced by 45 degrees. The cosine of a 45
degree angle is .7071. The power factor is .7071. This means the
circuit uses approximately 70% of the energy supplied by the
source and returns approximately 30%

 

 

R-L-C Circuit

Circuits often contain elements of resistance, inductance, and
capacitance. In an inductive AC circuit, current lags voltage by
90 degrees. In a AC capacitive circuit, current leads voltage by
90 degrees. It can be seen that inductance and capacitance
are 180 degrees apart. Since they are 180 degrees apart, one
element will cancel out all or part of the other element.

An AC circuit is

• Resistive if XL and XC are equal
• Inductive if XL is greater than XC
• Capacitive if XC is greater than XL

Calculating Total Impedance in a Series R-L-C Circuit The following formula is used to calculate total impedance of a circuit containing resistance, capacitance, and inductance

In the case where inductive reactance is greater than capacitive
reactance, subtracting XC from XL results in a positive number.
The positive phase angle is an indicator that the net circuit
reactance is inductive, and current lags voltage In the case where capacitive reactance is greater than inductive reactance, subtracting XC from XL results in a negative number The negative phase angle is an indicator that the net circuit reactance is capacitive and current leads voltage. In either case the value squared will result in positive number

Calculating Reactance and Impedance in a Series R-L-C Circuit In the following 120 volt, 60 hertz circuit, resistance is 1000 Ω, inductance is 5 mh, and capacitance is 2 μF. To calculate total impedance, first calculate the value of XL and XC, then impedance can be calculated

Calculating Circuit Current in a Series R-L-C Circuit

Ohm’s Law can be applied to calculate total circuit current

Parallel R-L-C Circuit Total impedance (Zt) can be calculated in a parallel R-L-C circuit if values of resistance and reactance are known. One method of calculating impedance involves first calculating total current then using the following formula

Zt = Et / It

Total current is the vector sum of current flowing through the
resistance plus, the difference between inductive current and
capacitive current. This is expressed in the following formula

In the following 120 volt, 60 hertz circuit, capacitive reactance
has been calculated to be 25 Ω and inductive reactance
50 Ω. Resistance is 1000 Ω. A simple application of Ohm’s Law
will find the branch currents. Remember, voltage is constant
throughout a parallel circuit.

Once the branch currents are known, total current can be calculated.

Impedance is now found with an application of Ohm’s Law.

 

 

 

Inductive and Capacitive Reactance

 Inductive and Capacitive Reactance

In a purely resistive AC circuit, opposition to current flow is
called resistance. In an AC circuit containing only inductance,
capacitance, or both, opposition to current flow is called
reactance. Total opposition to current flow in an AC circuit that
contains both reactance and resistance is called impedance,
designated by the symbol “Z”. Reactance and impedance are
expressed in ohms.

Inductive Reactance

Inductance only affects current flow when the current is
changing. Inductance produces a self-induced voltage (counter
emf) that opposes changes in current. In an AC circuit, current
is changing constantly. Inductance in an AC circuit, therefore,
causes a continual opposition. This opposition to current flow is
called inductive reactance and is designated by the symbol XL

Inductive reactance is dependent on the amount of inductance
and frequency. If frequency is low, current has more time
to reach a higher value before the polarity of the sine wave
reverses. If frequency is high, current has less time to reach
a higher value. In the following illustration, voltage remains
constant. Current rises to a higher value at a lower frequency
than a higher frequency

In a 60 hertz, 10 volt circuit containing a 10 mh inductor, the inductive reactance would be

XL = 2πfL

XL = 2 x 3.14 x 60 x 0.10

XL = 3.768 Ω

Phase Relationship between Current and Voltage in an Inductive Circuit

 Current does not rise at the same time as the source voltage in an inductive circuit. Current is delayed depending on the amount of inductance. In a purely resistive circuit, current and voltage rise and fall at the same time. They are said to be “in phase.” In this circuit there is no inductance. Resistance and impedance are the same

In a purely inductive circuit, current lags behind voltage by 90 degrees. Current and voltage are said to be “out of phase”. In this circuit, impedance and inductive reactance are the same

All inductive circuits have some amount of resistance. AC
current will lag somewhere between a purely resistive circuit,
and a purely inductive circuit. The exact amount of lag depends
on the ratio of resistance and inductive reactance. The more
resistive a circuit is, the closer it is to being in phase. The more
inductive a circuit is, the more out of phase it is. In the following
illustration, resistance and inductive reactance are equal.
Current lags voltage by 45 degrees

Calculating Impedance in a Capacitive Circuit The following formula is used to calculate impedance in a capacitive circuit

In the circuit illustrated above, resistance and capacitive reactance are each 10 ohms. Impedance is 14.1421 ohms.

The following vector illustrates the relationship between resistance and capacitive reactance of a circuit containing equal values of each. The angle between the vectors is the phase angle represented by the symbol θ. When capacitive reactance is equal to resistance the resultant angle is -45 degrees. It is this angle that determines how much current will lead voltage.

videos about inductive

Capacitance and Capacitors

 

 

Capacitance and Capacitors

Capacitance is a measure of a circuit’s ability to store an  electrical charge. A device manufactured to have a specific amount of capacitance is called a capacitor. A capacitor is made up of a pair of conductive plates separated by a thin layer of insulating material. Another name for the insulating material is dielectric material. When a voltage is applied to the plates, electrons are forced onto one plate. That plate has an excess of electrons while the other plate has a deficiency of electrons. The plate with an excess of electrons is negatively charged. The plate with a deficiency of electrons is positively charged.

Direct current cannot flow through the dielectric material because it is an insulator; however it can be used to charge a capacitor. Capacitors have a capacity to hold a specific quantity of electrons. The capacitance of a capacitor depends on the area of the plates, the distance between the plates, and the material of the dielectric. The unit of measurement for capacitance is farads (F). Capacitors usually are rated in μF (microfarads), or pF (picofarads).

Capacitor Circuit Symbols

Capacitance is usually indicated symbolically on an electrical drawing by a combination of a straight line with a curved line, or two straight lines

Simple Capacitive Circuit

In a resistive circuit, voltage change is considered instantaneous. If a capacitor is used, the voltage across the capacitor does not change as quickly. In the following circuit initially the switch is open and no voltage is applied to the capacitor. When the switch is closed, voltage across the capacitor will rise rapidly at first, then more slowly as the maximum value is approached. For the purpose of explanation a DC circuit is used

Capacitive Time Constant

The time required for voltage to rise to its maximum value in a circuit containing capacitance is determined by the product of capacitance, in farads, times resistance, in ohms. This product is the time constant of a capacitive circuit. The time constant gives the time in seconds required for voltage across the capacitor to reach 63.2% of its maximum value. When the switch is closed in the previous circuit, voltage will be applied. During the first time constant, voltage will rise to 63.2% of its maximum value When the switch is closed in the previous circuit, voltage will be applied. During the first time constant, voltage will rise to 63.2% of its maximum value During the second time constant, voltage will rise to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for voltage across the capacitor to reach its maximum value.

 

Similarly, during this same time, it will take five time constants for current through the resistor to reach zero

Calculating the Time Constant of a Capacitive Circuit

To determine the time constant of a capacitive circuit, use one of the following formulas

τ (in seconds) = R (megohms) x C (microfarads

τ (in microseconds) = R (megohms) x C (picofarads

In the following illustration, C1 is equal to 2 μF, and R1 is equal to 10 Ω. When the switch is closed, it will take 20 microseconds for voltage across the capacitor to rise from zero to 63.2% of its maximum value. It will take five time constants, 100 microseconds for this voltage to rise to its maximum value

Formula for Series Capacitors

Connecting capacitors in series decreases total capacitance The effect is like increasing the space between the plates. The formula for series capacitors is similar to the formula for parallel resistors. In the following circuit, an AC generator supplies electrical power to three capacitors. Total  capacitance  is calculated using the following formula

Formula for Parallel Capacitors

In the following circuit, an AC generator is used to supply electrical power to three capacitors. Total capacitance is calculated using the following formula:

videos about capacitors

 

 

 

 

 

series and parallel resistors

DC Series Circuit

A series circuit is formed when any number of resistors are connected end-to-end so that there is only one path for current to flow. The resistors can be actual resistors or other devices that have resistance. The following illustration shows four resistors connected end-to-end. There is one path of current flow from the negative terminal of the battery through R4, R3 R2, R1 returning to the positive terminal

Formula for Series Resistance

The values of resistance add in a series circuit. If a 4 Ω resistor is placed in series with a 6 Ω resistor, the total value will be 10 Ω. This is true when other types of resistive devices are placed in series. The mathematical formula for resistance in series is

R t = R1 + R2 + R3 + R4 + R5

 

Rt = R1 + R2 + R3 + R4 + R5

Rt = 11,000 + 2,000 + 2,000 + 100 + 1,000

Rt = 16,100 Ω

Current in a Series Circuit

The equation for total resistance in a series circuit allows us to simplify a circuit. Using Ohm’s Law, the value of current can be calculated. Current is the same anywhere it is measured in a series circuit.

Voltage in a Series Circuit

Voltage can be measured across each of the resistors in a circuit. The voltage across a resistor is referred to as a voltage drop. A German physicist, Kirchhoff, formulated a law which states the sum of the voltage drops across the resistances of a closed circuit equals the total voltage applied to the circuit. In the following illustration, four equal value resistors of 1.5 Ω each  have been placed in series with a 12 volt battery. Ohm’s Law can be applied to show that each resistor will “drop” an equal amount of voltage

First, solve for total resistance

Rt = R1 + R2 + R3 + R4

Rt = 1.5 + 1.5 + 1.5 + 1.5

Rt = 6 Ω

I = E / R = 12/ 6 =2

I = 2 Amps

E = I x R

E = 2 x 1.5

E = 3 Volts

Voltage Division in a Series Circuit

It is often desirable to use a voltage potential that is lower than the supply voltage. To do this, a voltage divider, similar to the one illustrated, can be used. The battery represents Ein which in this case is 50 volts. The desired voltage is represented by Eout which mathematically works out to be 40 volts. To calculate this voltage, first solve for total resistance

Rt = R1 + R2

Rt = 5 + 20

Rt = 25 Ω

I = Ein / Rt = 50/ 25 =2 amp

Eout = I x R2

Eout = 2 x 20

Eout = 40 Volts

Resistance in a Parallel Circuit

A parallel circuit is formed when two or more resistances are placed in a circuit side-by-side so that current can flow through more than one path. The illustration shows two resistors placed  side-by-side. There are two paths of current flow. One path is from the negative terminal of the battery through R1 returning to the positive terminal. The second path is from the negative terminal of the battery through R2 returning to the positive terminal of the battery

Formula for Equal Value Resistors in a Parallel Circuit To determine the total resistance when resistors are of equal value in a parallel circuit, use the following formula

Rt = Value of any one Resistor / Number of Resistors

In the following illustration there are three 15 Ω resistors. The total resistance is

Rt = Value of any one Resistor / Number of Resistors

Rt = 15 / 3 = 5 Ω

Formula for Unequal Resistors in a Parallel Circuit

There are two formulas to determine total resistance for unequal value resistors in a parallel circuit. The first formula is used when there are three or more resistors. The formula can be extended for any number of resistors

In the following illustration there are three resistors, each of different value. The total resistance is

The second formula is used when there are only two resistors

 

 

In the following illustration there are two resistors, each of different value. The total resistance is

Voltage in a Parallel Circuit

When resistors are placed in parallel across a voltage source the voltage is the same across each resistor. In the following illustration three resistors are placed in parallel across a 12 volt battery. Each resistor has 12 volts available to it

Total current in a parallel circuit is equal to the sum of the current in each branch. The following formula applies to current in a parallel circuit

It = I1 + I2 + I3

Current Flow with Equal Value Resistors in a Parallel Circuit

When equal resistances are placed in a parallel circuit opposition to current flow is the same in each branch. In the following circuit R1 and R2 are of equal value. If total current (It) is 10 amps, then 5 amps would flow through R1 and 5 amps would flow through R2.

When unequal value resistors are placed in a parallel circuit opposition to current flow is not the same in every circuit branch. Current is greater through the path of least resistance.In the following circuit R1 is 40 Ω and R2 is 20 Ω. Small values of resistance means less opposition to current flow. More current will flow through R2 than R1

Using Ohm’s Law, the total current for each circuit can be calculated

I 1 = E /R 1  = 120 / 40 = 3 A

I 2 = E / R 2  = 120 / 20 = 6 A

It = I1 + I2 =3 Amps + 6 Amps = 9 A

 

 

 

Lecture - 1 Introduction to Basic Electronics

Lecture - 2 Electronic Devices 1

resistors

can be used to control voltage and current in circuit

there are some types of resistors

(1) fixed resistors it has constant amount of resistance

* carbon resistors

* wire wire wound resistors

*ceramic resistors

the law to calculate resistive of resistors

the figure of resistors

 

 

( 2 ) variable resistors

we can adjust the amount of resistance

there are many types of it like

* lap type wire wound

* bench built

* centre tap resistors

* rheostat

* potentiometer

 

 

 

OHMs law

the current passes through resistance equal voltage drops    around resistance by resistance