^Sign of work
^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
in time 
This is independent of mass of block.^Forces in circular motion
When seen from inertial frame two types of forces act is a circular motion, one that changes speed & the other that changes direction.
A force that acts tangential of velocity changes the speed only, called tangential force. Its
magnitude is given by
A force acting normal to velocity towards turning centre, along the radius & changes direction is called centripetal force or radial force.
It is not a different type of force. It is actually the resultant of the forces acting on a system & directed towards the center of the circle. For planet revolving around sun gravitational force is centripetal. For a string whirled in a horizontal circle tension in the string is centripetal force. For oscillating pendulum resultant of tension in the string & normal component of weight is centripetal.
Example 1
The electrostatic force of attraction between electrons & nucleus changes the direction of electrons revolving around the nucleus thus we can write
FCP = Felctrostatic
Example 2
Gravitational force of attraction between the moon & the earth changes the direction of moon thus we can
write, FCP = Fgravitational
Example 3
Magnitude of centripetal force on a mass moving with velocity v in a circular path of radius r at constant speed (i.e. uniform circular motion) is
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.
Semiconducting devices are the basic building blocks of all the modern electronic circuits & have following advantages over conventional vacuum tubes:
^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.
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
^Zener diode
It is a specially designed junction diode, which can operate in the reverse breakdown voltage region continuously without being damaged. In forward bias behaves like ordinary diode. Zener diode does not gets damaged at breakdown voltage, but it does so at some higher reverse voltage, known as its ‘burn out value’. The magnitude of zener voltage VZ can be decreased by increasing doping level in p and n type materials of zener diode.
I – V characteristics of a Zener diode are as shown. For a voltage more than zener breakdown voltage current through diode increases without increase in voltage across it. This feature is exploited to provide voltage stabilization across a circuit.
Suppose a load RL connected between a & b is connected to a fluctuating dc voltage supply Vs between c & d. Let the load can’t tolerate a voltage VL but the supply Vs can be more than VL. To protect the load from any increase voltage a zener diode of breaking voltage VZ = VL is connected to the input supply with a safety resistor RS in the input loop.
If at any time VZ increases than VL the zener diode works in the breakdown region increasing the current through it without increasing the voltage across it & thus the load always remains protected.
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