## ^Examples of zero,  +ve & -ve work

^Examples of zero,  +ve & -ve work

Zero work means either no displacement of system no net change in the KE of the system. Few examples of zero work are

1. If there is no motion, no work has been done no matter how much force is applied.
2. A static person e.g.  a gate keeper does no work, as his displacement is zero.
3. Work done by normal forces (any force that changes only direction) is always zero e.g. work  done by tension in the sting simple pendulum, by your weight while walking on a horizontal surface, by normal reaction on a body.
4. Work done by a gas during its free expansion.
5. Work done by a magnetic field in moving a charge in a circle.
6. Gravity does positive work on an descending mass, negative work on an ascending mass & zero work for both for horizontal motion & cyclic path.
7. Consider the case of a weight lifter. He does,
8. (a) positive work to lift as he lifts weights the weights up (to pull weights up along the displacement against the gravity)
9. (b) no work, to hold the weights at their position (as no displacement means, no work )
10. (c) negative work to bring weights down at         constant speed (as he has to pull opposite to displacement to maintain speed)

## ^Motion on a rough inclined plane

^Motion on a rough inclined plane

Consider a body placed on a rough inclined plane.

The y component of the gravitational pull mg cosθ presses the plane & is balanced by normal reaction from the plane, thus N = mg cosθ.

The x component of the gravitational pull mg sinθ (say, F) tends to move the block down the plane, but can do so, only if it exceeds the limiting friction (fL = msmg cosθ) on the block.

As the inclination θ is increased mgsinθ increases while the limiting frictional force (mS mg cosθ) decreases. At one stage, mgsinθ & mS mg cosθ become equal & balance each other then the body placed of the inclined plane at the verge of motion. If the block at this stage is given some velocity it will keep sliding down at constant velocity.

This angle θ is called angle of repose & abbreviated by

symbol β. At θ = β,

or    mg sin θ = mS mg cosθ

or    tanβ = μS

Also we can make following conclusions

1. If θ < β, then F < fL & block remains at rest. Friction on block is static & equals mg sinθ.
2. If θ = β, then F = fL & block remains at rest. Friction on block is static & equals mg sinθ or msmg cosθ.
3. If θ > β, then friction acting on the block is kinetic mK mg cosθ. This is less than mg sinθ & the block slides down the incline with a uniform acceleration. Using kinematic equations for UAM it can be checked that a block starting from rest will strike the ground with speed in time This is independent of mass of block.
4. If the inclined plane is smooth (i.e. μ = 0), then the acceleration of a body sliding down a of inclination is, a = g sin θ
5.  Retardation by friction on a rough horizontal surface (i.e. θ = 00) is, a = μ g
6. The force required to move the block up along the inclined plane with const. acceleration a is, F = mgsinθ + μmgcosθ + ma

## ^Centrifugal force

^Centrifugal force

A pseudo force experienced due to change in direction is called centrifugal force. Centripetal force is a real force while centrifugal force is pseudo. Mathematically both are equal in magnitude.

## ^Centrifugal force

^Centrifugal force

A pseudo force experienced due to change in direction is called centrifugal force. Centripetal force is a real force while centrifugal force is pseudo. Mathematically both are equal in magnitude.

## ^Logic Gates

### ^Logic Gates

Basic building blocks of digital electronics made of semiconducting material & used to control the flow of information from input to output in a logical manner & are used in calculators, digital watches, computers, robots, industrial control systems, and in telecommunications.

## ^SCs Versus VT devices

### ^SCs Versus VT devices

Semiconducting devices are the basic building blocks of all the modern electronic circuits & have following advantages over conventional vacuum tubes:

1. don’ require a heating battery & thus set in to operation as soon as the circuit is switched on.
2. require comparatively low voltage for their operation.
3. don’t produce any humming noise during their operation.
4. shock proof, small & compact in size, cheaper than vacuum tubes, have a very long life & are free from vacuum deterioration trouble.

### Limitations

1. higher noise level.
2. can’t handle as much as power as ordinary tubes can.
3. poor response in high frequency range.
4. temperature sensitive (maxi. tolerance 50 0C).

## ^Oscillator

^Oscillator

An oscillator is self sustained transistor amplifier with a positive feedback which produce electric oscillation of constant frequency

& amplitude without requiring any external input signal. It converts dc energy obtained from a battery into ac energy in same oscillatory circuit.

## ^CEA

#### Output is 1800 out of phase with input.

Transconductance is also called mutual conductance.

As β > > α, thus the ac power gain of a CEA is much larger than that of a CBA. Remember the transistor is not generating any power. The energy for the higher ac power at the output is supplied by the battery.

Saturation state:

Both the junction are forward biased & here IC is maximum & does not depend on the input current IB.

Cut off state:  Both the junctions are reverse biased as a result IC = 0. Between cut off & saturation state a transistor works as switch as here it turns over rapidly from OFF state (i.e. IC = 0 or cut off) to the ON state (i.e. IC is maximum or saturation state).

Active state: Emitter base junction is forward biased and the collector base junction is reverse biased. A transistor works as an audio amplifier in this regions.

Relation between α and β:

As the value of IB is about 1 – 5 % of IE or IC is 95 – 99 % of IE, α is about 0.95 and 0.99 and β is about 20 to 100.  It is found that α and β are independent of current if the emitter base junction is forward biased and the collector base junction is reverse biased. Also the above definitions of α and β do not hold when both the junctions of a transistor are forward biased or reverse biased.

The CE configuration is frequently used as it gives high current gain as well as voltage gain.

## ^Transistor

^Transistor

1. Emitter is the section on one side of transistor that supplies charge carriers. It is of moderate size & heavily doped. Collector is the section on the other side of transistor that collects the charge carriers. It is moderately doped but larger in size. Base is the middle section of transistor that forms two pn junctions with emitter and collector. It is very thin and lightly doped so as to pass most of the emitter injected charge carriers to the collector.
2. A transistor is also called Bipolar Junction Transistor (BJT), as in it current is due to both majority & minority charge carriers.
3. Input of a transistor is always forward biased, output is reverse biased & the common terminal is grounded.
4. Current in both npn & pnp transistor is IE = IB + IC. As the base current IB is very small thus IE » IC.. A transistor transfer almost the same electric current from low resistance path to high resistance path and hence is named as transistor. This transistor action makes it useful in transistor amplifier.
5. A transistor can be used as a switch, amplifier, oscillator & NOT gate.
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