3. (a) A potentiometer wire AB has a length 0.5 m and resistance 0.5 ohm. As shown in figure , it is connected with a cell Of e.m.f. and a combination of resistance R = S = 5 ohm.  Find 
the potential drop per unit length of the wire. 

 

We can first find potential drop across the potentiometer wire and then divide by length to find potential drop per unit length.
To find poential drop of wire we have to first find current in the circuit.
       I=V/R
      V=3V
      R= 3ohm ( 5 ohm and 5 ohm in parallel in series with 0.5)
     therefore, i=3/3 = 1 amp
    Potential drop across wire = i * resistance of wire 
                                               =1*0.5
                                               =0.5V
  potential drop per unit length = 0.5/length=0.5/0.5 = 1V/m = 0.01V/cm
 

Thanks Ashek