43.MET April 2019 Q.6(b)

A moving coil ammeter, a thermal ammeter and a rectifier are connected in series with a resistor across a 110 V sinusoidal ac supply. The circuit has a resistance of 50 Ω to current in one direction and, due to rectifier , an infinite resistance to current in the reverse direction. Calculate 
a) The readings on ammeter
b) The form and peak factor of current wave

           If you are noticing some error in problems kindly comment below.Thanks

Given

V = 110V
R = 50 Ω

To find

a) The readings on ammeter
b) The form and peak factor of current wave

Solution

a) We know that

V = 0.707 x Vmax

So Maximum voltage,

Vmax = V / 0.707
          = 110 / 0.707
          = 155.5 V

As per Ohm's Law Maximum Current

Imax = Vmax / R
         = 155.5 / 50
         = 3.11 A

As we know that moving coil ammeter, a thermal ammeter and a rectifier connected in series with a resistor across an ac supply.

So during positive half cycle average value of current

Iavg = 0.637 x Imax
        = 0.637 x 3.11
        = 1.98 A

During negative half cycle the current value is zero. But due to inertia of moving parts the moving coil ammeter will show the average value of current through the whole cycle

Reading on the moving coil ammeter = Iavg / 2
                                                            = 1.98 / 2
                                                            = 0.99 A

Reading on ammeter is proportional to heating effect

So during positive half cycle average heating effect 

Havg = (1/2) x I²max x R

During negative half cycle the heat dissipated is zero. But the thermal ammeter will show the average value of heat through the whole cycle

Reading on thermal ammeter = [(1/2) x I²max x R] /2
                                                = (1/4) x I²max x R -------------------------------(1)

Total heating effect = I² x R ------------------------------------(2)

Equating (1) & (2)

I² x R = (1/4) x I²max x R

I = Imax / 2
  = 3.11 / 2
  = 1.55 A

Reading on thermal ammeter = 1.55 A

b) Form factor kf = I / Iavg
                           = 1.55 / 0.99
                           = 1.57 

    Peak factor kp = Imax / I
                            = 3.11 / 1.55
                            = 2.0