Chapter #2 :Vectors : Short Q/A / C.R.Q's

Q. Can a vector has zero magnitude if one of its components is not zero?
Ans:No A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:-If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay  then A=0+Ay A=Ay

Q. Can the resultant of two vectors of the same magnitude  be  equal to the magnitude of either of the vectors? Give mathematical reasons for your answer.
Ans. Yes. If the angle between these two vectors is 120 degrees than it is possible.
For example:-  Consider two vector having magnitude A then
R=√A2+A2+2 A.A CosÎ¸         If R=A then    A=A√2Cos2Î¸/2
=> R=√2 A2+2 A2 CosÎ¸                     or 1=√2Cos2Î¸/2
R=√2 A2    (1+ CosÎ¸)               S.O.B.S
=> R=A√2Cos2Î¸/2                  1/2= Cos2Î¸ /2 then Î¸ /2 =60
Or Î¸=120 Degrees
Q. Can two vectors having different magnitudes be combined to give zero resultant? Can three vectors?
Ans. The Resultant of two vectors having different magnitudes can not equal to zero,If they have same magnitude and opposite direction then their resultant will be equal to zero.
Where as the resultant of three vectors equal to zero if they form triangle after combination.
Then A+B+C=0

Q. How is it possible that i,j and k are vectors but don’t have magnitude?
Ans. The Unit Vectors (i , j , k ) are used to show the direction of any vector and they don’t represent any physical quantity therefore they have no units.

Q. For Dot Product A.B=AB cosÎ¸. Why cosÎ¸?
Ans. The Dot product is “The product of magnitude of any vector to the magnitude of projection of  another vector”.In the mathematical formula The cosÎ¸  represents the projection of one vector over another along X-axis.

Q. If A x B =AB and A.B=0 then what is the angle?
Ans.     A X B =AB SinÎ¸                                A . B =AB CosÎ¸
If Î¸= 90 degrees                                              If Î¸= 90 degrees
Then    A X B= AB    (b/c Sin90=1)              Then A.B =0   (b/c Cos 90=0)

Q. Can the magnitude of any vector will be negative?
Ans. No the magnitude of any vector can not be negative because magnitude is calculated by
A=√ X2 +Y2 +Z2
So after squaring, if there is any negative sign it will be removed. hats why magnitude will not be negative

COMMON COLLECTOR CONFIGURATION OF A TRANSISTOR

COMMON COLLECTOR CONNECTION

In  this  configuration  the  input  is  applied  between the  base  and  the  collector and  the  output  is  taken  from  the  collector  and  the  emitter.  Here  the  collector  is common to both the input and the output circuits as shown in Fig.

Common Collector Transistor Circuit

In  common  collector  configuration  the  input  current  is  the  base current  IB  and  the output current is the emitter current IE. The ratio of change in emitter current to the  change in the base current is called current amplification factor.

It is represented by

COMMON COLLECTOR CIRCUIT

A test  circuit  for determining the  static characteristic  of an NPN transistor is shown in Fig. In this circuit the collector is common to both the input and the output circuits.   To   measure   the   base   and   the   emitter   currents,   milli   ammeters   are connected in series with the base and the emitter circuits. Voltmeters are connected   across the input an…