electrical engineering: Basic Electronics

Showing posts with label Basic Electronics. Show all posts

Tuesday, August 2, 2011

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%

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