Question

QUESTION 3 (a) Explain the difference between transformer electromotive force and motional electromotive force in electromagnetic. Write down the integral equation for both quantities. [4 marks] (b) A circular plate with radius, a meter at x-y plane rotates in an anti-clockwise direction with a uniform angular velocity, o meter/second along the z-axis. The plate is placed in a uniform magnetic flux density, B = Bâ, Tesla. Find the expression for the induced electromotive force at the rim in relative to the centre of the plate. [6 marks] A rectangular coil is placed at the x-y plane and moves from the origin along the +y axis (c) at a velocity, ū = 5â, ms'. Magnetic field in the region is given as B = 0.2e0â Tesla. If R = 102, calculate the current, I while the coil is in the location as shown in Figure Q3(c). [10 marks] 4.5m 4m 2m и 1m. У Figure Q3(c)

Explain the difference between transformer electromotive force and motional
electromotive force in electromagnetic. Write down the integral equation for both
quantities.

Answer 1

1. 
   * Transformer Electromotive force d + Let the fun at any instant be given by R 0 = om sincet) - The instantaneous emf induced in a coil of t turns linked by this then is given by Faraday's law as e= -d (QT) =-T dd =-T d (am Sinut)) dt at =-T w Om lasot (T= no. of turns) = Two msin (wt - 7/2) @ Equation 2 may be written as :- e = Em sin (wt-7/2) where £m = Twom = masimum value of e. for a sine wave the ums value of emf is given by Erms = E= Emilia os E=Twam = T (2xf) om r2 or E= 4444f0m T
   
   The emf induced in each winding of the transformer can be calculated from its emf equation. Let subsrift I and 2 be used for primary and Secondary quantities. The primary r.mos voltage is 1E,= 4:44 pmf Til (Ti = no. of turns in. - primary) ums voltage is The Seconday I 2 = 4.440 m f Tal where om is the manimum value of teen un webers (Wbli t is requeny in heit (Hz) & E, & Ez are in volts. If Bm= marimum thun density in the magnetic curmit (love) in Tesla (T) A = Area of cross section of the Core in square meters (m2 l
   
   from Bm = Om 's 4 esla = lwblm2 Motional Electromotive force fleen artz. If a rod of length I moves with velouty v in a direction perpendicular to uniform and time independent magnetic field B, an emf is induced in the roda As shown in figure wod X Y is there to. move on conductor ABCD. The nod XY is moved towards the right with a constant velouty v. Assume that the rod XY and the lonductor AB CD is Ariction less so that there w no less of The area enclosed by a REDMI NOTE 5 PRO MI DUAL CAMERA pwendu
   
   XBCY . Let the length XB be R. As area enclosed by XB CY changes, the magnetic feun enclosed by the loop XBCY is given by :- Po = BA Coas o = BA Lees 0° = BA= Bln As the magnetic fleen is changing, an emf will be induced. This ent is given by : E =-da B = -d (Bln) = - Bel da dt dt म where / dor = -1 is speed of Rod XY | E=-Bl.(-u) = Blv.
   
   ditterene between transformer.. ent and motional emf. Transtomer emf i Motional emf ③ - Equation b Equation E=нч фn +т E = BIV Om = manimiam value of sinusoidal fleen ta frequency T= no. of Twins. B = magnetic field (uniform and time independent) I= length of Conductor u= velocity of Conduc- -ctor in magnetic field. o Emt & Om at T for 6 This is tuse i emf induced 1 Transformer: in ® This is used tor to calulate emf induced in conductor is placed in mugnetic field.
   

10 defend when 14 depend upon electrical parameter Dynamic parametes such as Frequency such as velouty. teen of Mechanically | Electrical parameter on no. of turns. . Such as Magnetic field. depend upon length of Rod © It is © It is vector Scalar Quantity quantity