Solution for Question1 : IES Conventional 1998 : Electronics & Telecommunication Engineering : Paper I

Q.1: (a) Show that a semiconductor has minimum conductivity at a given temperature when  

Sol: To find the minimum conductivity, first consider the mass action law.

==>    

                 

Now, substitute for n in the equation of conductivity,

To find the value of p that gives minimum conductivity, differentiate the above equation with respect to p and equate it with 0.

==> 

                                         

Similarly, we can define,

                                            

Q.1: (b) When the current through a Zener diode increases from 20 mA to 30 mA the voltage across it changes from 5.6 V to 5.65 V. What is the voltage across the Zener when the cur rent is 35 mA ?  

Sol:  

Q.1: (d) A white noise is applied to an RC low pass filter. What is power spectral density of the output noise and what is its average power?

Sol: PSD of output Y(t) = Sr(f) = N0/2 ,             -B < f < B

                                             = 0 ,                   otherwise

Hence, PSD of output = Sr(f) = (N0/2)/(1 + (2.pi.R.C)2)

Output of average power of RC low pass filter = N0/4RC

Output of average power of I low pass filter = N0B

Output of average power of any filter = N0BH(0)

Q.1: (e) Find i1, i2, and v in the circuit of Fig. 

Sol: Consider the three nodes in the circuit as shown below, and apply KCL at these nodes i.e. X, Y and Z.

At node X, 
                                                 I2 + 2 A = 8 A
                               =>                       I2 = 6 A

At node Y, 
                                                  2 A = 2 A + I
                               =>                       I = 3 A

At node Z, 
                                                   I2  = I1 + I
                               =>                       I1 = 3 A

                                    V = 3 I2 + (-2)(4) = 3(6) - 8 = 10 V