Rectifier Circuit, Rectifier Theory, Half Wave Rectifier, Full Wave Rectifier, Rectifier Diode

Rectifier Circuit, Rectifier Theory, Half Wave Rectifier, Full Wave Rectifier, Rectifier Diode

RECTIFIER: The circuit which converts AC into DC is called Rectifier Circuit.

There are basically two types of Rectifier Circuit:

1)      Half wave Rectifier

2)      Full wave Rectifier

(a)    Centre Tap Full Wave Rectifier

(b)   Bridge Full Wave Rectifier

1). HALF WAVE RECTIFIER

This is the simplest Rectifier Circuit. The circuit has only one diode.

IN POSITIVE CYCLE OF THE INPUT AC VOLTAGE:

When the input voltage is positive the anode of diode is +ve and the cathode of diode is –ve. This results in forward biasing of the diode. When the diode is forward bias it behaves as a short circuit. As a result we get the input voltage at the output of the circuit. As a result we get the input voltage at the output of the circuit.

IN NEGATIVE CYCLE OF THE INPUT VOLTAGE

When the inputs reverse its cycle the anode of the diode become –ve. This reverse biases the diode. As a result the diode behaves as open circuit. No current can flow in the circuit and the output voltage we get is zero.

PERFORMANCE OF HALF WAVE RECTIFIER

The current wave of half wave rectifier

THE TOTAL RMS VALUE:

RIPPLE FACTOR (r):

RECTIFICATION EFFICIENCY (ŋ):

FULL WAVE RECTIFIER

There are two types of Full wave rectifier:

(a)  CENTRE TAP RECTIFIER

(b)  BRIDGE RECTIFIER

(a) CENTRE TAP RECTIFIER

Centre tap rectifier uses a centre tap transformer, two diodes D1 and D2.

DURING +VE HAALF CYCLE:

At this time the polarity of the two voltages Vs will be shown in figure below:

With this polarity D1 will be forwarded biased and D2 will be reverse biased. D1 will behave as short circuit and D2 will be open circuit.

The current will flow in the upper part of the circuit and no current will flow in the lower part. The current will flow through the load in the shown direction and the polarity of the voltage drop in the load will be as shown in the figure above.

DURING –VE HALF CYCLE:

During –ve half cycle the D1 will be open circuit and D2 will be short circuit. The current in the circuit is as shown in the fig. Note the direction of current is same through the load resistance as the current is +ve half cycle. As the current is unidirectional in the complete cycle we can say we have got a DC

PEAK INVERSE VOLTAGE (PIV)

It is the largest reverse voltage that is expected to appear across the diode. In centre tap rectifier the PIV of each diode should be 2 Vm where Vm is the peak input voltage at the secondary of transformer.

(b) BRIDGE RECTIFIER

DURING +VE CYCLE

            In this input diodes D1 and D3 are forward bias. The flow of current will be as shown in figure below:

DURING –VE CYCLE

            At this moment diodes D2 and D4 are forward bias and D1 and D3 are reverse bias. The flow of current will be as shown in figure below.

The flow of current is unidirectional therefore the voltage developed across the load is DC.

PEAK INVERSE VOLTAGE (PIV)

PIV of the diodes used in the circuit is Vm.

Performance of Full-wave Rectifier

            The DC Value:

The Total RMS Value: 

              Ripple Factor: 

              Rectification Efficiency:

Relativistic Addition of Velocity, Addition of Velocities, Addition of Velocity in Relativity

RELATIVISTIC ADDITION OF VELOCITIES - ADDITION OF VELOCITIES - ADDITION OF VELOCITY IN RELATIVITY

Consider a frame of reference s’ moving with uniform velocity v relative to a stationary frame s along the positive x direction. A particle is moving along the positive direction of x axis with a velocity given by dx/dt as observed by an observer in frame s.

As observed by an observer in frame s’, he distance travelled in dx’ in time dt’- the velocity of the particle as seen by the observer in observer s’ is given by

To find a transformation between u’ and u we use Lorentz-Transformation which are as follows:

Differentiating Eq. (2) and (3) w.r.t t’, we obtain

Rearranging Eq. (4) and using Eq. (8)

Equation (9) represents the relativistic addition formula. The inverse relation will be given by

Consider two photons approaching each other such that the velocity of each photon as observed by a stationary observer is c. In order to calculate the relative velocity of one photon w.r.t  another

Thus for photon B the relative speed of photon A is equal to "c". 

Time Dilation is Real Effect, Time Dilation in Relativity, What is Time Dilation?

TIME DILATION IS A REAL EFFECT - TIME DILATION IN RELATIVITY - WHAT IS TIME DILATION?

Time Dilation concept has been experimentally verified by an example of cosmic ray particles called mesons. Mu Mesons are created at high altitude in the earth atmosphere (=10 km) by the fast cosmic ray photons and are projected towards the earth surface with a very high speed of about m/sec which is 0.998 c. Mu mesons are unstable and decay into electron or positron with an average life time of about .

Hence in its life time a Mu meson can travel a distance

But the question is that Mu meson travel a distance of 10 km to reach the earth surface. This is possible by time dilation.

In its own frame, Mu mesons have an average life time is 

.

Now 

This example explains the presence of Mu mesons on the earth. Hence we can say that time dilation is real effect. 

Time Dilation, Time Dilation in Relativity, What is Time Dilation?

TIME DILATION – TIME DILATION IN RELATIVITY

The word dilate means “Enlarge beyond normal size”. Time is also not absolute but relative. It is found that a moving clock in the space craft appear to tick at a slower rate than the stationary one on the ground as seen by an observer on ground.

Thus if a clock moves with very high speed v relative to an observer then it appears to be slowed down or time to time interval is increased by a factor .

Let us consider two frame of reference s and s’. s’ is moving with velocity v relative to s which is at rest along +x direction. A clock is at point x in the frames. Let the clock give out signal at two instant t1 and t2 then the interval between signal is given by .

If the signal interval is observed in frame of reference s’ then interval  is given by

From Lorentz transformation equation for time

Hence for a moving observer, the time interval appear to be dilated (increased).This phenomenon is known as Time Dilation.

Michelson-Morley Experiment, Michelson Interferometer, Morley Interferometer

Michelson-Morley Experiment, Michelson Interferometer, Morley Interferometer

ETHER HYPOTHESIS

A material medium is a necessity for the propagation of waves. It was considered that light propagate through ether as the sound wave propagate through air. Ether affects all space. An interesting question is whether relative motion between the earth and ether can be detected. If such a motion can be detected, we can choose a fixed frame of reference in stationary ether. In 1887, Michelson and Morley set out to measure the relative velocity of earth with respect to the ether. The principle of the experiment lies is nothing, the shift in fringes in Michelson Interferometer due to the difference in time taken by light to travel along and opposite the direction of motion of the earth. The time taken by a beam of light to travel along the direction of motion of earth is greater than that of traveled  distance opposite to the direction of earth. Surprisingly, despite best efforts, the presence of ether could not be detected.

MICHELSON-MORLEY EXPERIMENT

The main aim of Michelson-Morley Experiment was to find evidence confirming the presence of an absolute Frame of Reference called Ether. Ether was thought of as a medium which fill all spaces and penetrates all matter. It was considered to be rigid, Invisible, Mass less and perfectly transparent elastic, non-resistive, continuous and with negligible density.

Michelson’s Interferometer consists of two plane mirrors M1 and M2 arranged perpendicular to create coherent sources by division of amplitude. The light from the sources goes to the beam splitter P and then divides itself to go to M1 and M2 separately. The reflected light mirror M1 and M2 is allowed to interfere and interference fringes are observed.

The two mirrors M1 and M2 are placed at equal distance  from the plate. It is assumed that the earth is moving through the ether with velocity along the direction of the incident light.

Due to the motion of the apparatus with the motion of earth, the time taken by ray 1 travelling to mirror M1 and ray 2 travelling to mirror M2 would not be the same.

If c is the velocity of light through ether, then using Galilean Transformation, the velocity of light along the direction of incident light is c-v for light from P to M2 and c+v for light from M2 to P also 

The whole apparatus was rotated by 90 degree and the fringe pattern was observed to measure the amount of fringe shift.

Due to rotation of apparatus,

The expected fringe shift was evaluated using the formula in Equ ..(6) and was calculated to be 0.4 but actually even though the experiment was done very precisely and number of times, no fringe shift was observed. This null result could not be explained by Michelson and Morley at that point of time.

EXPLANATION OF NEGATIVE RESULT

1.   ETHER-DRAG HYPOTHESIS: The hypothesis assumed that ether moved along with the earth while the later moved through space. Thus there was no relative motion between the earth and ether. This implied that the fringe shift goes to zero.

2. FITZGERALD-LORENTZ CONTRACTION HYPOTHESIS: Lorentz and Fitzgerald put forth the suggestion that there was contraction of bodies along the direction of their motion through the ether by a factor of 

.This hypothesis was rejected because it was purely mathematical and had no experimental evidence to support itself.

3. CONSTANCY OF THE SPEED OF LIGHT: In order to preserve the ether hypothesis it was proposed that light travel with a constant speed with respect to the source. This was in contradiction to the wave theory, thus a negative result of the Michelson-Morley experiment could not be explained through the proposed hypothesis at that time.